Or does a harder difficulty just make things more challenging?

Technically it does increase the value of the loot as it is harder to get, but all the objects you get have the same stats/value..

The reason why it won't affect the loot is that you could change difficulty all the time, so in combat you play at the easiest but when looting it's on the hardest and you get the best loot. So no, it most likely doesn't.

It makes me spend all my money for potions, recipes and trainers. So yes, affects a lot.

Playin' max difficulty from the start so I don't really know.