[verb て-form] + くれない? [verb て-form] + くれませんか [verb て-form] + もらえない? [verb て-form] + もらえませんか
てくれない? and てもらえない? ask someone to do something for you: "could you", "won't you". They follow a verb in the て-form. A negative question leaves the listener room to say no, so it sounds softer than a straight order.
The plain forms are for friends and family. The polite forms end in ませんか: てくれませんか, てもらえませんか.
These go beyond asking a favour.
With falling intonation and no question, the same words are a plain negative: "he won't do it for me". The rising tone and the question mark make it a request.
Said sharply, a request like this can carry annoyance: "would you mind…".