Strange Card Behaviour

AstonSmith

I work in a shop and we take card payments. Lately I've noticed a few odd things happening. Can anyone comment on these situations and my questions below?

Customer A: Contactless payment attempt causes the machine to request the card be inserted (two short beeps). Upon doing so, it doesn't request the PIN like usual - instead it immediately connects to the card processor and declines. A was unable to pay with that card.

Customer B: Contactless fails in same way as A. B inserts the card, and it signals that it's the last PIN try. B enters a PIN. Machine connects to the processor and requests a signature. Approved. Every payment with the card since then has behaved like a chip and signature card (sans contactless functionality).
Customer C: Customer was able to pay by swiping the magnetic strip, even though the card had a chip on it.

A says the card works in every other shop and in cash machines. Is this our fault? Other peoples' cards from the same bank process fine.
I think B has locked their card with three invalid PIN entries. If so, why is it still approving with a signature? I advised B to try resetting the PIN in a cash machine, but at the moment they are either unable or unwilling to.
I thought swiping chipped cards wasn't supposed to work and instead request chip and PIN be used. Could C's card be some sort of clone (via re-recorded strip), or am I being paranoid? Are my assumptions wrong?