Welcome here, KisforKeyboard. I hope you enjoy your stay here.
As for learning TI-BASIC there are a few good sources around. There is
TIBD (TI-BASIC Developer) which is probably one of the best places for individual command learning and such. Another great way to learn is to just look over some code from games and such. That way you can see how things work and get a feel for it. Also, as yunhua98 said, I have some tutorials for here that can help get you started but I have also made a thread that has the links to them along with the other tutorials on this site, and other places,
here.
As for learning Axe. It is a much faster language than TI-BASIC (Pure and Hybrid) but it can also be a bit harder to learn if you don't understand the concepts behind pointers and such and although it is recommended that you learn TI-BASIC a bit before it is by no means required (especially if you program in other languages and have experience from those already). But Axe is a wonderful language that people around here have really taken a liking to.
xLib is an assembly library which is essentially just a program that installs a hook (I believe) that lets you use a certain TI-BASIC command and it will run an assembly routine when the TI-BASIC program hits it. It is a very useful application that has been used a lot. I believe tr1p1ea is the one who created it, but I'm not entirely sure. Progress on it, to my knowledge, has been stopped though and the latest version, again to my knowledge, is v0.602b. You'd have to find the original thread or someone else that knows more about that. But as I kinda said it is used for Hybrid TI-BASIC to help run faster and with better graphics and all.
As for Pokemon. Ya, there are already a few versions being worked on. FinaleTI has one in Hybrid TI-BASIC, tifreak has one in Hybrid TI-BASIC too though it's all ASCII sprites and such (except for battles and such), and Madskillz has an assembly clone of Red being worked on. The game that you found, or your friend found, is one by JoeYoung (formally Metagross) and he isn't around Omnimaga due to some issues (he's been banned). But that was before my time so you'd have to ask one for the older members for details on that (probably DJ since he is the one who told me). He is active over at UTI though, I believe. But I'm not 100% sure.
Yu-Gi-Oh though I don't think I've ever seen being worked on but it'd be quite the feat to do with all the information that needs to be stored, but good luck.
I would also suggest maybe not start with a big project if you're pretty new to TI-BASIC as it can just get overwhelming and such. I'm not saying you can't do it as it's been done before, just don't want you to get discouraged or anything
Good luck on any projects you start though and can't wait to see what you can come up with. Hope you enjoy it here
Edit:
The lobster thing is another meme around here. It's a running joke that Netham45 is a blue lobster. Long story that I don't even really get either
But ya, as yunhua98 said, the peanuts are another meme in which new users get a bag of peanuts. I think DJ said it started in 2004 (?) and ya. I'm not the greatest historian on the memes
Also ya, please try to use the Modify button that is located up in the top right corner of your posts or the quick modify button that is located in the post off to the right side. For a look at the Double Posting rule check out
Rule #3.