-Pokemon Centers function as both a hospital (for humans and Pokemon, should there be a need for it) and a motel of sorts for trainers, offering rooms to sleep/stay in as long as they need as well as basic amenities like a food court and hygienic facilities. Depending on where they’re located determines how big and how advanced they are (ex. Mauville City’s PokeCenter would be a lot bigger and better than Dewford’s). They can get fairly large and are fully staffed at all times through funding by the Pokemon League.
-PokeMarts are more similar to all-around general stores for trainers, and while in-game you can’t normally purchase things like evolutionary stones and special items/accessories, they’re just much more expensive and not easily accessible to normal trainers. A trainer can also purchase camping supplies (like fire kindling, sleeping bags, et cetera because of how long some of the routes are) and Mega-stones if they’re, again, in a bigger city like Slateport or Mauville - but those are basically for the richest of trainers because they’re so rare.
-I think the six-carry rule is stupid and wouldn’t be realistic because the ‘Pokeball getting sent to a PC’ concept is very dubious to me, so I scrapped my character using the storage system altogether in favor of the fact that she has a place she chooses to send them to instead, should she desire it. She can thus carry as many Pokemon as she wants, though she doesn’t have too many over six to begin with. She has a similar device she carries that she can place a Pokeball inside and send it to her home, but that’s about it. To amend the ‘six-only’ rule, however, I established it as a rule for Pokemon battles between trainers, otherwise you can be fined by the League for cheating.
--The same would apply to moves - I think Pokemon remember every move they learn, but you can only actively use four in battle. HMs also apply to this. (To discard the need for HM slaves because that would be kind of cruel for actual Pokemon.)
-All around, the continent realistically would be much, much bigger than what is represented in-game, and I take after the anime in that respect (though I don’t add additional cities because they’re not in the focus of the story and I don’t think there would be any, except maybe small barely-towns along the bigger routes or on the outskirts of cities). This is why it takes up to a full day for my character to travel from Mauville to Fortree, not even including the Southern Island incident.
-Brendan and May stick together throughout their journey instead of splitting up, thus the reason why they don’t have much interaction with Gemma. (Brendan also may have a small - tiny, mind you - teeny weeny crush on Gemma, as is evident by his shaky first greeting with her in the prologue. May teases him about it a lot, so he avoids Gemma as best he’s able.)