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 (+25%) for a matching set.
- Dawnguard Light - 25% less damage from Vampires and Drain Life spells
- Dawnguard Heavy - same bonus
- Ahzidal's Armor - 10% Enchanting with the boots + exactly 3 other items from the set of 7. More or less than 3 other items will not activate the bonus.
- Deathbrand Armor - each piece's enchantment gets stronger when wearing more pieces of the set
Also from Dragonborn, but weapons:
- Soulrender and Bloodscythe - absorb health and magicka, chance to reduce armor and dispel magic when used together
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.
Some followers have perks. These are not listed on the Elder Scrolls Pages, generally, but a GameFAQs forum user was kind enough to use the Creation Kit to identify and list them. This list is four years old, so it could be out of date if patches have changed things.
Based on that list, there are eight followers that have perks that give them bonuses for full sets of armor:
25% armor bonus if wearing all Heavy Armor: head, chest, hands, feet
Tower of Strength
50% less stagger when wearing only Heavy Armor
25% armor bonus if wearing all Light Armor: head, chest, hands, feet
Belrand, Karliah, Mercer Frey, Celann, Durak, Serana
The Ahzidal set works with the boots and any other 3 relics(dragon priest mask, helmet, armor, gauntlets and rings). Only a total of 4 items equipped, though. Equip 5 items and it cancels the effect. Deathbrand armor requires dual wielding for the one handed bonus to work.
There is a hidden bonus to both the nightingale armor set and the shrouded armor set. When you wear all 4 pieces of either set you get an extra 25 points of armor. Not that great since there is no perk that lets you improve them twice as much, but with smithing skill, gear and a potion should make it easier to hit the armor cap(just need more light armor perks).
There are set bonuses in skyrim, with or without the DLC, for instance, wearing a full set of Daedric Armor increases your intimidation stat checks by 10%, which means you only need to meet 90% of their required points, to be able to intimidate. You can see this on the wiki's and test them in game, as I have.