Can I make purchases with Apple cash

To clarify. If the website you wish to buy from supports Apple Pay, then you can select the Apple Cash card like you would other cards in Wallet to pay from. See here: link-> Make purchases using Apple Pay - Apple Support

If the website does not support Apple Pay, then you cannot use Apple Cash.

Depends on the merchant. Some will decline the purchase. Other will use the Cash amount with the balance remaining for you to cover. It will not move the balance to your Apple Card automatically.

You cannot use Apple Cash online as there is no card number associated with the card.