In the Bazar - when you buy credits - Do you pay them then they transfer credits to you?

That's usually how it's done. You pay, then they transfer the credits to you. Though, if people make arrangements to pay by check or money order or something like that that's sent by mail, often a deal will be made to send some or half the credits in advance while both parties wait on the mail service to do its job. Otherwise, there'd be a delay of days before the buyer gets any benefit.

I've sold credits a few times and was paid by Paypal, once the money came through, I transferred the credits - can all be done very quickly. 

I suggest timing the transfer of money to when you will both be near a computer. Then send a PM after you do the transfer so they can check the paypal account as the email from paypal takes a little while telling them about the transfer.