This really, really depends on how the game is designed. If swimming is very integral, and often comes up, and the designers are too lazy to give the dungeon multiple pathways while maintaining good level design, then it should probably be possible. I voted only at master, though, it doesn't really matter: how does it make sense to swim with heavy armor in your pack, but not wearing it? Should probably be based on encumbrance vs buoyancy instead.
Big fatigue loss with running and jumping: hell yea.
Rolls and flips: hell nay (with out without heavy armor-- what is this TWitcher?).
Burden at master level: I voted no, but heavily dependent on the game itself. Maybe partially.
Penalty to sneaking: Yes. The immersionistas, realtatos, hardcorporals, and rollerplasters should all be in agreement over this one.