In example, if I make my companion wear full set of Dwarven armor, will she get some kind of reward bonus (like in Diablo) for wearing full set?
The only armors that have a sort of "set bonus" are in the DLCs. All other armors only have the perk bonuses for a matching set.
Also from Dragonborn, but weapons:
No, there are not armor set bonuses in Skyrim.
The closest thing is a range of perks that will improve various attributes when wearing a full set from a particular category. This wiki page details this towards the bottom of the page.
However, perks obviously don't affect your companion.