1. From the posts above it seems like the A3 Cyprus version is a debit card, which means one needs the funds available in their daily account for transactions to be approved. So there is no risk from the bank's side, and hence they might be willing to provide to non-residents or people without an income generated in Cyprus, as long as that person has deposited sufficient funds into the account.
2.
I doubt that any bank in the world would give you a credit card for a country that you don't live in and have no income in.
Well, that's inaccurate. In Thailand some banks will provide a credit card even without residency or working there, provided the applicant has left a deposit with bank. The monthly usage limit is set equal to the deposit, and funds will be withdrawn from that deposit to cover any unpaid credit transactions. So again, no risk as far as the bank is concerned.