Do the heroes have same-sex relationship autonomously? Like, I have this spy who is best friend with the royal advisor, if I leave them alone, would they autonomously start romantic actions on their own and become couple? or do I have to start them meself? do the sims even start romantic relationship(both straight & gay) on their own?

Each sim has a preferance value that moves when romantic socials are used. They start mostly straight, but after a few directed socials their preferance can be changed. These values are used in figuring out what sex a sim in TS3 will persue, but I don't think I've ever seen a sim in Medieval autonomously use a romantic social (lots of friendly hugs and sword fights). I believe in this game it only influences success in directed romantic socials.

Well, I have seen to male NPC's kissing before and hugging. So yes, they must do.

Are you sure they kissed? I see them hug, or try to hug all the time, but the only kissing I've seen is in relationships that I created. Once the relationship is created they do autonomous socials. Considering they can't have children or get married I assumed EA had removed the code. Maybe my kindoms are just filled with un-romantic sims.

Yea, I see a lot of friendly hug, comforting hug and sword fight but I've never seen any who start romantic actions on their own...=( I hope I'm wrong and they do though because even though I don't mind building the relationship till best friend, I actually hope to see them start the romantic acts on their own xD... like move onto the next level on their own and stuff, it just feels nicer and exciting that way. yea I'm weird like that. 8D

I've seen one of my hero female sims who had her first kiss with another female autonomously flirt with the monarch's female servant! They didn't kiss but they were doing the flirt actions/reactions (woo, swooning)

It's strange that they would do that. I would be upset to come back from questing with my monarch only to find my knight was romancing sims I didn't approve. I'm assuming that's why it never reaches a kiss, because I think I may have seen some autonomous flirting going on. If the sims kiss an actual relationship is created, so since I've never come back to a hero to find they had a new romance, I don't think they can kiss or beyond.

My knight and his wife will kiss and hug autonomously but I've never seen other sims go beyond the flirting/bestowing favor on their own.

My monarch has the licentious trait and he "Complimented the ankles" on a male npc. This was after I directed him with a same-sex romantic interaction on another sim.