How does the dating mechanic work? Is it like trying to match the idols up with someone? Can you date the idols?(18 and up) of course. Or is it just a random feature for them to randomly effect their mentality?

I also want to know how to date some idols, I just try speaking and that increase the friendship but at lvl 4 I flirt and didn't work, maybe my character is just ugly? Or we have to change the dating polity? 

They have gender preferences. Your character might not be her type.
Ive been reading through a lot of the mod stuff.

I don't think that the dating system was yet be implemented in the game.

Two of my idols feel for each other but im not sure how to date them your self.

Dating hasn't been added to the game yet. You can flirt with them and level up the romance to the point where they'll start flirting back, but the proper dating system is not live yet (except when it's idol-idol or idol-stranger relationships)