Look, it's impossible for anybody here to explain to you how particular court will work, unless somebody has been in it. So, we can only give you general pointers, and it's up to you to see what's going on in there. Just sit in on one of the sessions, and you will hear all sorts of crazy stories, see a few traffic attorneys and what you can and cannot do.
To answer your questions: you can always motion, but if you are in a magistrate court, most rules don't apply, and your motion can be ignored or denied for no reason. If you are facing the judge or not even the judge but some clerk, you know you are in trouble. If, on the other hand, you hear something like "anybody who wants to talk to prosecutor/DA/officer before trial begins" or just get invited into a room with a table and two chairs, you have a plea bargain, AKA shortcut in procedure where you get a small break in exchange for saving the court time. You don't just demand the plea bargain. Sometimes you can ask if you can talk to DA before trial. You can even call the officer, at any time, and explain that you are a poor student, and cannot afford the fine, etc. He may just take mercy on you, and make the ticket disappear. Try it, it does not hurt any, since you got nothing to loose.