Well there isn´t much difference, but "love me do" basically means "Please love me". In english "do" isn´t used like this much anymore these days but you´ll mostly hear it as an answer form though for example "Do you mind if I hang my coat here?" "No, please do" (in other words: please do it, please go ahead, feel free etc) I hope I got this right!?!

It's not proper grammar. I'm assuming it's that way for artistic reasons.

Oh~! sorry~! I don't know. I want to mean.