For example:
On the website you can buy altcoins with BTC or Eth. Would it be possible for customers to buy them instantly? I guess no, because it takes time for Btc or Eth transactions to go through blockchain and get confirmed. We can't release our altcoins if we don't get a payment confirmation.
Is there any way around? For faster transaction confirmations?
of course you can, actually the transaction on the exchange will not be recorded by the blockchain, its inner the exchange, they just account inside, if you withdraw your money, it will be recorded and confirmed by the blockchain