Overall energy gain boost is unique trait and is provided only by the river set.
Game have several more energy management mechanics like starting energy or fury so it's can't be answered shortly, I suggest to read ingame description of stats on any hero.
Energy regen is not in the runes stat table as Health regen as well. Those 2 stats are totally useless so no big deal.
And bout your 3rd question - his damage reduction is scaling of skill level.
So you can only improve it by equiping runes with expertise.