Isn’t it right that bitcoins transactions are only confirmed when a block is mined?

Normal bitcoin website explain it like this: "Roughly every ten minutes, a new block is created and added to the blockchain through the mining process. This block verifies and records any new transactions. The transactions are then said to have been confirmed by the Bitcoin network." So really how could the network confirm it, without new blocks?

So when we hit 21.000.000 and there are no blocks to mine, how will you transfer your bitcoin if it can’t be confirmed?

Quote from: buybitcoinworldwide.com/confirmations

Please share reliable sources when trying to help find a solution. Thank you!