Learn English – Why do we have to use ‘have got’ instead of ‘got’

You would get the same answer to each question whether you used would or does; both questions ask for the price of the action mentioned. There is a slight difference in the implication of why you're asking, but the information you want is the same.

When you ask How much does it cost to [x], you're simply asking for information. You could be asking out of pure curiosity, or because you want to purchase the item in question, but no implication is made either way.

When you ask How much would it cost to [x], there is a stronger implication that you're wanting to buy the item you're discussing. Instead of a straight pricing inquiry, you're saying "If I were to buy [x], how much would it cost me?" Using would introduces a future conditional, thus the implication that you're considering the purchase (based on the answer to the question about price).

The verb construction have got is used to convey the meaning of possession. So the sentence 'He has got the car' means that he is in possession of the car.

Simply got however, means something a different. It is synonymous to to obtain or to receive, which is what happens before someone becomes possessor of something.

This gives the following difference in meaning in your sentence:

If he has got the car, he will visit New Jersey. = If he is in possession of the car, he will visit New Jersey.

If he had got the car, he would visit New Jersey. = If he was in possession of the car, he would visit New Jersey.

You cannot use got here in your sentence, because it is used to refer to obtaining something in the past.

Instead, you could say:

If he were given the car, he would visit New Jersey.