AAAAAAA. Okay, hi hi hi! Yesterday was a very important day for me, and something I had to get through before I could return to roleplaying. But, huzzah! Believe has arrived! With school starting in only a few days, I'm excited that I'll actually have a SCHEDULE, and therefore, won't have issues where I only respond sometimes.
Anyways, moves! Now, first of all, I had an idea for TMs/HMs being similar to the games--but, due to the suggestion of watching TMs like a training video, I totally want to go with that. It's a super cute and clever proposal, and plus, learning moves from videos is perfect for a school. It could be like homework!
Second, let's talk about the four-moves limit. In this universe, Pokemon can learn more than four (depending on the mental capacity of the creature; just, remember, don't go overboard. You don't need thirty moves!) BUT for a lot of the competitive world, it is understood (from Kanto all the way to Alola) that battles take place with only four moves. Essentially, for a gym challenge or something, you would have to submit paperwork (or some other strenuous task) with your moves you will be using on it. If you use moves outside of this pool that you have entered with, you end up nullifying your battle (or disqualifying yourself from a contest.) Pokeathlons don't exactly use moves, so don't worry about that too much. There might be special Pokeathlon events at the Capelle Pokeathlon (yep, we'll be hosting our own!) that require special moves or types, but all typical events will be similar to the games. There are some situations (like extremely casual battles) where Pokemon will use more than a moveset of four, but in, well, everything else, four moves are required. Ms. Capelle didn't exactly worry too much about using more than four moves in the icebreaker, and since this IS a school (which will offer many opportunities to learn new moves) I didn't require you list your moveset in your bio for this reason. Now, do keep in mind, your Pokemon can only learn moves that its species can have, and unless you have the proper parents, you can't randomly give your Pokemon an egg move. Also, the moves don't have to match how they appear in the games! For example, look at how our lovely little Floatzel used Protect. She inflated the yellow around her neck to protect her, instead of making some... weird... psychic shield thing. You get the point. Just remember that in the future, your Pokemon will only be able to use a set of four moves for certain challenges and the like! (That was a rule probably put in place by the Pokemon League in order to keep things fair.)
Finally, I want to mention levels. I think it's a good time to bring it up. Levels are NOT used in this universe, and ages are completely separate from levels. In essence, if you want to teach your teenage Wooper Muddy Water (which it learns at level 47) you probably shouldn't. Adult Woopers (or even Quagsire) would be a better fit to learn this move. A child won't be able to use extremely powerful attacks! Plus, when it comes to general evolution (as friendship or item based evolutions are a little different) your Pokemon will naturally evolve after a certain amount of training in this universe. For the purpose of the roleplay, it will be after two years of schooling, or four total seasons. (Reminder that years in the school do not reflect actual years; it is simply how we judge who is in what grade.) Also, if your Pokemon fails a year, they won't be able to evolve until they actually complete it. :c For Pokemon with third evolutions, it will reach its final evolution after three years (six seasons.) Let's... for the sake of simplicity, leave Megas out of this.
I hope that answers all your questions! If I wasn't clear on certain parts (as I have a tendency to ramble through my explanations) or you have any extra questions, feel free to ask. And, as always, I ADORE the art that was made. It's like... "zomg wowza someone made FANART for my roleplay?????"