He likely does because the other Monster Trio members have it. I also think that Jimbei will awaken his during Laugh Tale Arc

His dream is to find the All Blue, and this isn't a kingly desire.

He is the cooKing

I doubt it. Doesn’t seem necessary

No way he’s not a conqueror person. Do you want me to tell you the idea of having a conqueror haki my theory is that to have that conquerors is that you have ambition for Sanji he’ll give up on his ambition for woman