[rtkwe]

No not at all. Miners are the ones generating blocks and validating them though the giant distributed work they each do. Without miners there would be no new blocks which means no verified transactions. The only place trades could still happen is on exchanges because they all happen off block and don't rely on the blockchain to track who owns what but it'd be impossible to move more coins onto or out of an exchange so you'd be stuck.

[yks]

what happens when all possible bitcoins are mined then?

[rtkwe]

Miners will be paid with transaction fees. Already if you don't include a fee in your transaction you can expect much longer transaction confirmation times or to never receive confirmation because miners already try to pack the most fees into each single block to maximize their payout.