You're afraid you're not normal? Well that's the most normal thing you've said! You adults all have the same worries and insecurities. So before you even ask, let me answer your questions once and for all...actually I'll probably still have to remind you, because these questions are persistent! Here are your answers:
Yes, you can do this
There are very few people in the universe who are actually incapable of learning the piano. It's not magical at all. It's similar to wondering "Am I really capable of learning Spanish?" Yes. Almost anyone can. It might take longer than you expect, but it takes roughly the same amount of time for everyone. And everyone feels like it shouldn't take so long. True, there are people who are incapable of learning a new language. And there are some who learn languages freakishly quickly. But that has nothing to do with you. You're normal. This will take some work, but you can totally do this!
No, you don't suck
...as long as you're comparing yourself to you. How's your financial situation? If you only have a few million saved, you're a pauper compared to the thousands of wall street executives, movie stars, and sports heroes who regularly throw away your net worth on a game of blackjack. But If you're a homeless person in California sleeping on the streets, you're still making more in year than 98% of the world's population.
Because music is a language, there is no best in music any more than best in English. How would you even help someone become the best at English? Speaking the fastest? Largest vocabulary? Most persuasive? Most elloquent? Most entertaining? Best spelling? Where do you even start? Hello? Hi? What's up? Howdy? Depending on your goals, even starting with one of these might be considered terrible by another teacher: "Can you believe that guy? he started with 'Hi!' - that's not even proper! I always teach my students 'Hello'. 'Hi' isn't even proper English. That teacher is doing more damage than good." I've heard music teachers talk this way about other teachers. I guess when you make a living at something that doesn't really matter, you have to go a long way to try to make it seem like it matters.
This music thing isn't a game of comparison. There's no prizes. There's nothing to win. It's a language. You learn to speak it so you can use it. It's a tool for you to express yourself and create experiences. It's impossible for YOU to suck. This isn't about you. It's about the music. And no, the music doesn't suck. You only sucked at understanding what the music is there for. Stop it! ...There. Now you don't suck anymore.
No, you're not failing
You can't fail. "Failure" is about academic evaluations (like tests or homework, where the objective is to get something into a person's head) and I'm talking about mechanical movements. Babies learning to walk, kids learning new sports, teens learning to drive, etc. Incorporating new mechanics is just an accepted, necessary part of their lives. Even video games are kind of built on the premise that the player will fail at the correct movements/timing hundreds or thousands of times in a row (and you'll notice there aren't nearly as many new gamers over 40). And as far as I know, Kim Jong Un is the only person who has hit 18 holes-in-one on his first game.
But even in academics, while test scores may be high (implied: only a little 'failure'), the whole premise of test preparation is that if you tried now, you would fail, so you're going to fail many times before the test [study] until you aren't failing those terms/questions/dates anymore so you don't fail during the test. Then consider that on the first day of school, every 14 year-old student accepts that there will be a test on subject x in order to move to the next level. Tell a group of 34 year old employees they're going to have to take a test on literally anything new, and some of them will be so scared they will opt to search for another job rather than be evaluated like that.
THAT is why you get the whole "aww - good for you!" vibe from anyone talking about adult education. Especially in mechanics, but even in academics, taking on new things that might include some 'failure' is more uncommon the higher the age. But you're trying so - awww - good for you!
Yes, you are talented
That is, if you believe in such a thing. It would seem from tons of research that Talent either doesn't exist or is, at least, way over-rated. In my experience, talent is largely the obsession with a specific topic or skill. The more obsessed a person is, the more talented they seem to be. You're obsessed enough to be reading a blog post about learning piano. That's crazy. You're sick. Congratulations! You're talented.
Drive to focused practice and a vision for the goal - if that's not talent I don't know what is. Some people can force themselves to it, but the desire to continue to do it is really what will really sets a student apart. Then add the ability to objectively compare your playing to the ideal of what it should sound like instead of just following instructions mechanically? That student is going places. YOU are going places.
No, you're not special. Yes, I've seen that before.
Whatever weird coincidence you have found that makes you think your circumstance is special, you're probably wrong. It's probably mildly interesting at best. You always learned songs quickly when you were a kid? You think you have an eclectic taste in music? It's really hard to play both hands together? It's harder to play with your ring finger? You've already forgotten a song you worked on recently? You still remember a song you learned as a kid?
Yep. Normal. Normal. Normal. Normal. Bad news? You're not as special as you thought. Good news? There's nothing actually holding you back from learning this little music thing.
No, you don't have to start on piano to play guitar or another instrument
Piano IS much more visual than other instruments, so music theory usually makes more sense on a piano than other instruments. Also, wherever you're going, there's probably a piano there, and it'll be cool to be able to play it. Also, it's probably the most common instrument to learn, so whatever other instrument your friends play, they probably have a cursory knowledge of piano. In that way, it's kind of the Rosetta Stone for musicians. When saxophonists and tuba players are having a hard time talking about their parts with each other, they're going to end up discussing it at a piano.
So yeah, there's lots of great reasons to start on piano. Another big one is that the piano takes zero talent to create perfect sound. Press any one of the keys and bam! ...you've got a perfect note. That's not true for most other instruments: guitar, saxophone, flute, violin, trumpet - nearly all instruments require a ton of work just to learn to make a sound. On piano, you're off and running from day one.
But ultimately, the best instrument to practice is the one that you're motivated to practice. If you're dying to play drums, play drums. If you are in love with the sound of the acoustic guitar, strum away, my friend. Strum away!
Yes, finger exercises might help
...but probably not as much as you think. To whatever extent your early-onset arthritis can be eased up with some flexing, go for it, but the majority of what feels like finger disobedience isn't age, it's un-coordination. That's fixed with practice. And finger exercises can help with that over time, but it's not like doing a little each day is going to help each day. Doing a little each day is going to help...in eight months as you start to become more and more coordinated.
Finger flexibility is not a universal problem for adults. The biggest obstacle by far for adults is the mental hurdle. Once expectations are reasonable and the desire is still there, I've had students push through a ton! From arthritis, to blindness to hearing impairments...I've even had several students who were missing fingers and arms! But they all struggle with feelings like "I should be making progress faster than this," or "My granddaughter can play better than I can." Whether it's music or finances or relationships or any other endeavor in life: not comparing ourselves to others is tough. Most everything else is just excuses...?
No, your fingers aren't too short/long/thick/weak
Despite your great aunt's insistence, "piano fingers" aren't a thing. Long, slender fingers can reach farther but are frequently weaker and less coordinated. Short, stubby fingers can be faster and more nimble, but can't reach common intervals. You know which fingers are best for piano? Fingers that have practiced! But you saw that coming, didn't you?
Yes, you will learn music theory
It's a serious let down to me, but this is a legitimate question. Apparently some teachers don't teach theory!?! I can't even imagine such an experience, but if you're hanging out anywhere near me, it's going to leak out all over the place. I have a insatiable need for my students to know why and how and when. To me it would be like teaching language without acknowledging that some words represent things, and others represent actions, and others describe things. And don't get me started on words that join!!
No, you don't have to learn to read sheet music
Everyone, and I mean EVERYONE is sure this is the most important skill. But the majority of adult students don't need nearly as much of this as they think. Back to the language analogy: imagine someone telling you they want to be a captivating story teller at parties, so they really want to learn how to read. Those might be somewhat related skills, but the quickest path to being the life of the party is NOT sounding out letters.
"But I've heard there are some really entertaining stories in books and I want to tell good stories like that! Won't that work?" Um...yes. That could work, but it's also entirely possible you'll be able to read and still suck at parties. Why don't we skip the alphabet for now and just work on some story telling techniques and then we can slowly work on this reading thing on the side?
Not that I would ever advocate for illiteracy, but learning to read has, as it turns out, surprising little to do with speaking well. Which is why we teach babies how to speak and don't really harp on learning to read until 5 or 6 years later. And even then, we give them a good 5-10 years before we expect the whole literacy thing to really blossom.
Yes it's normal to take this long
You're chasing the sunset. It looks catch-able, but it's not. The only option is to enjoy the journey. Record yourself. Not because you're good enough, but precisely because you're bad. In 6 months, you'll need to hear what bad sounded like to convince yourself you're making progress. When you remind yourself how bad you used to be, you'll start to realize: No matter how good I get, I'm always going to feel like I'm on the verge of being good.
No, you're not too old
You're so young! I mean that sincerely. From the perspective of music, whatever your age, it's a fine time to start. I have students EVERY week starting their first lesson who are 65 and over...way over. There will be phases of more and less practice; more and less progress, but stick with it as long as you enjoy it. Age don't make a difference. If you got 2 years under you're belt, you're way ahead of 99% of the population.
It's just that there's a lot of people out there, so no matter how good you are, there are always millions better. Like this ridiculous kid: Joey Alexander. I may never attain what he's already capable of...we'll see. My golden rule of internet talent is: whatever your age and whatever your skill, there's always someone on the internet who is half your age and twice your proficiency.
But if you enjoy the journey, it doesn't matter where others are on theirs. Their abundance of ability doesn't take away a microgram of ability I get to enjoy. I don't enjoy the sunset any less, knowing that others have seen more beautiful sunsets than the one I'm looking at.
Conclusion
Jump in. The water's fine. You're fine. It's all fine. Enjoy the wins and persevere through the struggles. The answer is always more practice. More time. More patience. More being-slightly-better-than-yesterday. You can do it. Good luck. Have fun!