"I morgen køber min far en bil for mig" would mean that he buys a car on your behalf. That is, you're paying for it, but you don't have the opportunity to go to the dealership yourself, so your dad does the buying for you.
If you wanted to say that your dad buys a car for you as a gift, you could say: "I morgen køber min far en bil til mig."
I now understand the V2 order when reading sentences, but always forget to do it when producing the sentences myself. Would it also be correct if I put adverb at the end? e.g. 'Min far køber mig en bil i morgen'?
Yeah that's correct. You only invert the word order when you have like a phrase before the main part of the sentence
A few sentences ago "køber" translated as the verb "shop". I thought the father and the child were going shopping for a car.