Is it rude to ask someone how much they paid for something?

It's generally considered a bit personal to ask straight up, but the context matters here. Since you're mates, he might not mind at all - some people are pretty open about it, others get weird about money stuff. I'd say feel it out: if he's been bragging about the car or seems excited to talk about it, he'll probably be fine with the question. If you're still unsure, you could ask something less direct like "did you get a good deal on it?" which gives him an opening to share the price if he wants to without putting him on the spot.