On #1, call the court (or show up in person) and ask the court clerk. The day of the cite does not count, nor do holidays or weekends. Since day of was a holiday/didn't count day combined, they had until January 8th to file it.
#3 is a definite no. My opinion is never pay for what you can do yourself. It is an unnecessary extra cost to you. If you are eligible and wish to defer, all you need to do is get on the contested calendar. Most judges explain the whole deferral process, then have people who wish to defer line up. The judge will confirm your eligibility and grant it based on that. You usually pay a slightly higher fine.
When you get your discovery response, redact your personal info and post the entire thing so we can have a look at it and see if there are any technical attacks you can muster.

