Creating a 'cloned' physical second card with contactless capability is technically very difficult and quite rare due to having to replicate the encryption technology contained in the chip. Cards with magstripes containing unencrypted data are much more easily cloned but you need to put the card in to a skimming machine - this is why this happens a lot at cash machines, petrol stations, bars etc where you hand over your card to an unscrupulous actor.. What can happen today is that your contactless signal can be relayed via a transmitter to a payment terminal which is fooled in to thinking your card is present and a purchase that is already in progress is authorised. Same principle for stealing cars where the keyless signal is amplified from where the key is to where it needs to be to open the car.
It should yes, as it will refuse to provide the positive confirmation that the terminal is asking for. Card data can be harvested in many other ways though - stealing of data when making online purchases or hacking card data held unsecurely by organisations is a greater risk.
How about having a pre paid Mastercard https://www.mastercard.com/gb/en/personal/find-a-card/prepaid-card.html
