A) You were guilty, even if you just pay it by mail, you're still being found guilty, it's just easier since you don't have to show up.
B) When I've gone to traffic court, the people who have had expired tags license whatever usually get the ticket waived if they show up proving they've gotten it renewed or fixed or whatever.
C) I think even if you pay the ticket by mail or phone you still have to pay court costs.