Not an attorney, so this isn't legal advice.
No... you cannot fire your agent, now that they've brought you a buyer. But you do have the right to simply respond with a resounding 'no', when the buyer asks for you to pay more than you want to for repairs, or 'whatever the buyer wants'.
If you want to contact the buyer on your own, I suppose you could do that (no rules against it), but you will still owe your real estate agent/agency the commission that you signed for on your exclusive marketing agreement.
Yes, the buyer has their own agent... that's the way it normally works. The buyer found your home and photos online, and scheduled a showing through the efforts of your agent.