Are we supposed to root for them?

I find the characters in this show very interesting. Perhaps Marco being the most lackluster of the main characters. Yes they have all done some morally gray or even bad things but that's just because they live in perilous days. Staying in power often required one to use any means necessary. I don't expect people in historical shows to act according to current day morals.

of all questions, why did kokachin surrendered herself to get drowned? She should've went away with Marco, that's what i thought when i saw her going away from the tent. But getting suicide or surrendering herself to Empress like that for what?

I think she realised at the end that she f@cked up her life beyond repairs. She was devastated by the fact she got no one, even marco left her, the one person who truly cared for her. She was raped and given birth to kids who will never know their true father. She lost her identity "Nergui", even though she was a peasant girl THAT was her true identity. The real blue princess haunts her in illusions and dreams. Kokachin's storyline was the most upsetting of all of them.

She should've taken the kids and gone with Marco! but he's back though to find her drowned and dead.

This is just like "Game of Thrones": from their own perspective, everyone thinks him/herself as "the good one", but everyone is a killer/thief/rapist/etc.

Even 100 eyes, the most beloved guy in the show, is a cold blooded assassin.