Did vs have

Jerry: Did you get my card? I sent you a card on behalf of me and my family. You didn’t get it?

Kevin: Maybe. I didn’t check my mailbox.

(The card was sent a week ago)

Would "have" be better in place of "did" in any of the three places?

Did you get my card? / Have you received my card?

You didn't get it? / You haven't received it?

I didn't check my mailbox. / I haven't checked my mailbox.