I actually was just discussing this with someone about this last night. So, I'll talk a little about it.
A couple things to note though. You said gen specifically, but I'm going to talk about tiers too. Even between an OU and UU tier there can be huge differences. Also, I'm going to mostly use Gen 1 OU as an example, because that's generally considered the "main tier" on here.
how many different types of curves are there?
Are there different curves for different generations?
Short answer: Yes.
Long answer: Just from the perspective of what one needs to know to be decent at the tier, every tier has different things that are more important to learn than others, even if the mechanics are the same. If we quickly compare Gen 1 OU and Gen 4 OU, for example, being able to predict an opponent's team/core is vastly more important in Gen 4 OU.
When looking at "mastering" the tier, the differences become so much different that there's not even a comparison. Gen 1 OU has a learning curve of playing around Reflect Chansey, which obvious doesn't exist in anywhere else.
Is it possible to assess my skill 4, 5, 6 years from now?
Short answer: No.
Long answer: People grow at different rates, hit different plateaus and get through said plateaus at different speeds (some never get over certain plateaus as well). Sometimes it has nothing to do with how much plays or trains, but it has to do with other outside factors, even genes/personality. People are too varied to make an accurate guess half a decade down the line. Especially if the goal is to make a one size fits most kind of guess.
How easy are some generations to pick up?
Short answer: Most generations are going to be the same, give or take. There are definitely people who will fight me on that though.
Long answer: I would say that all gens have a lot to learn and are deceptivly deep. As for what is easier, that all depends on where you come from. I started playing long before team preview, so that's not something I have to worry about. I already understand the lead meta, etc. However, for a lot of players who came in durring XY, SM or even BW, this can be another hurdle (or learning curve, since we're on the subject), making these tiers harder to pick up for them.
At the same time, I don't play a lot with Fairy-types and so it's not something I really remember well, and other types like Poison have a much different utility in my mind. This is fine when I play ORAS NU casually, but it's definitely something that keeps me from playing at the next level. So, even an old gener vs new gener kind of mentality doesn't work.
how easy are some generations to Master?
I think you have to define master, because everyone will probably have a different perspective on how that word should be defined. Thus meaning that you'll never be able to get an answer as people are constantly talking past each other.
Can we graph learning curves of past players to create an estimate for a new player?
Short Anwer: Maybe, but with a lot of work and imperical evidence, which is effort better spent elsewhere.
Long answer: Scientifically speaking, in order to adjust for different people's different backgrounds, interests, personalities, etc. we'd need hundreds of players to learn in an controlled enviroment, and chart their progress. We'd also have to figure out how we wish to define different progress points and what would be important information to graph in the first place. Even if we used peer-reviewed data involving mastering a skill, etc. we'd still need to do ground work on figuring out how that would best apply to pokemon. If you really want an accurate chart, that would be years of work with no compensation. I guess you could go to your local university and see if a Pokemon loving Ph.D student would want to do their disertation on something like this. But I don't a review committee would pass them, and being a Ph.D student is already hard enough.
Now, if you really want your chart and don't care much about accuracy. I guess you could make random guesses, based on anecdotal evidence. But then, what was the point in making the chart in the first place? It's not going to be accurate and isn't actually useful.
Why do some people plateau whilst some people continue to develop?
Short Anwer: Everyone plateaus. How, when and why all depends on a long list of factors ranging from genes to interest to previous experience.
Long answer: Everyone is going to plateau at all the things they do. If you haven't plateaued at something yet, then you haven't done the best you can yet. Why? Well, there are so many reasons and factors involving why one may plateau at a certain point, that you have to look at it from a case by case basis. You may be able to make list of generalities, but they'd have to be vagued, and person would have to be honest with themselves on a persoanl level to figure out which ones kinda apply to them. That's going to be the equivilent of Buzzfeed and Facebook quizes though.
Is age a factor in learning curves?
Short answer: Yes. However, it may not be how you think, and that doesn't mean you can't get over it.
Long Answer: The way age affects one's ability to learn has to do with how developed the brain is (the brain stops developing around the age of 24-26, but the brain has different stages at which somethings are more optimal to learn at and is generally speaking the younger the better) and how much ability the brain has lost -like when your great grandmother can't figure out how they get electricity on planes. My psych background is with linguistics, so I'm not an expert on when exactly which periods are best to learn a strategy game. However, there is probably information out there. Just use Google Scholar (and if you need help reading a scientific paper I could quickly explain it).
However, sometimes thinking that age is stopping you from learning something can be more detrimental than the age itself. Your preception and your brain's reality are sometimes the same thing, even if it differes from actual reality. If you think you can't learn something, your brain may perceive that as the reality of the situation and you won't learn it. Why should your brain waste precious resources trying something that it's going to fail at?
Mathematicians, get number crunching.
Just fyi, this is absoutely something for psychologists, not mathematicians. Yes, it involves stats, but every psychology undergrad is going to take multiple classes involving, learning and using stats. There's not a psychologist, worth their salt, that can't take this information and chart it, and everything outside of actually making the graph is psychology.
EDIT: I'm sure there are mistakes, but I don't really want to proofread this. Hope that's ok, and sorry if it isn't.