Do I need to remove my card from my wallet to validate it?

You don't have to take your card out of your wallet to validate it.

However, it should not be validated next to other contactless cards.

Otherwise, you run the risk of the validator triggering the validation (and balance consumption) of all the cards, of the card it recognises first (which may not be the one you wanted) or that none of them are validated, incurring all the risks inherent in this.