There was a poll on his Patreon regarding the difficulty of the fights. The one thing that for sure is going to change is, they're going to add a tutorial to better explain the mechanics of the fights, which will hopefully clear up a lot of the difficulty. But they will also be taking a look at the difficulty itself, and making some adjustments.
So to answer you question, no you only get the on health potion. HP goes up with Gina's level, so no you can't really increase HP if you're as high a level as the story allows for whatever fight you're getting into.