There is no difference

I wouldn't worry too much about this. They both communicate exactly the same thing. The technical difference: one uses the present partciple (repairing) to refer to the future and the other uses the infinitive of the verb to be + past participle. How much will this help you to communicate more effectively? Not one bit!

Yes, both work. Technically, "be repaired" is the passive voice, while "needs repairing" is the middle voice. In your example, either would work. If you also wants to mention the one who will repair, the passive would be more natural, "be repaired (by a mechanic)."

You can use both, but to me "needs repairing" doesn't sound as comfortable. It's not wrong, though.

Thanks !!