She seems like the brave type. Im sure she'll be able to befriend the Beast like Belle did.

She's not as gentle as Belle is, so I imagine Beast and Esmeralda would have more arguments, but still I believe Esmeralda would give him a chance.

I really can't picture her staying. She would have tried to run away as soon as possible. She tried to do that in the cathedral, but Frollo had guards at every door. The Beast didn't have anyone really guarding Belle, so if Esme was in her place, she would have left real quick.

^ I agree

I'd say she'd run away because she likes her freedom, but she would go back to help him, as long as he didn't make her stay there forever. I can't really imagine them falling in love though.

I can't see her prisoner of anybody. She says herself she can't be trapped in a place, she's a gypsy. I don't think she has Belle's patience, so she wouldn't stick around with Beast long enough to see his good side.