I have a feeling your starter is not going to follow you anywhere and everywhere. It's probably out of it's Pokéball only for some script/event, and is likely to disappear immediately after you complete the said event.
Right now, we don't really know. So far we have only seen a chickorita out of its pokeball, no other pokemon. So who knows what that was all about just yet?
As for new formes appearing in these remakes, highly doubtful. With the breeding going to introduce visual differences with pokemon, this will do away new formes for the moment. Take spinda and its spots, it did not have new formes for each spot, just the same pokemon with visual change in its spots.