I'll tell you the real deal, but this is only for CA (as far as I know)
* You get ONE extension, for 45 days. Ask for the extension, a MUST.
* Yes, you can just pay it off through the mail unless you have a possibility of getting your license revoked (second major, or third minor/major offense in 3 years). Call the court and ask (just to be safe). In your case your major is a carpoolviolation, but they wont revoke you for that. They revoke for speeding and DUI's.
* If you do go to court, you have a pleading. You plead guilty or not-guitly. If you plead guilty, well you just waisted your time and should have just sent payment through the mail.
* Side Note-Since your tints are a fix it you will have to at least stand in
line and show proof of signature. The sheriff at your local station can
sign it off.
* Here is what is most important. If a COP gave you a ticket, the guy isn't going to show. Seriously. Cops almost NEVER show up. Now, if it is a Chipper (CHP Officer) that gave you a ticket you are dust. Chippers are basically forced to show up, and they have to give an excuse NOT to go (ie-sick day, vacation leave, etc.) Cops don't have to show (althoguh they are encourageed to).
I have beaten all my tickets.
If you have never been to traffic school then opt for it with the judge. It will save your insurance from going up.