Yes, sell the car. I'd record what you're spending on the inspection, up keep, and everything, and put that extra money towards the principal on the student loans. And of course the 800 (or whatever you get on selling) towards that too. Think of it this way, you're already used to spending that money, so just put it towards paying off the 4.5% drain (or 8% when you factor in inflation). By paying that off, it's almost like investing in a guaranteed 4.5% investment. If your mom puts her foot down and says no, you have to keep a car; then say fine, but mom, you're buying it from me, and paying for the upkeep. Then maybe she'll see why you need to sell it. If she doesn't see it, well you've solved your problem either way.
I agree with going to the roth first. After that you can start saving/investing, as you'll now already be paying down the student loans faster with the money from the car. I'd recommend a bit larger emergency fund, as I doubt that 2k is 6 months of your living cost. Open up an online savings account, as they offer the best interest rates right now, just so you are getting something (no matter how negligible) while you build up your emergency fund. As for investing (after a bit larger emergency fund), the easiest and simplest strategy you'll find most people here give for when people say "hey I've got extra money, where should I put it?" without much more info, is in either the s&p 500 index fund (VFINX), or the total stock market fund (VTSMX), via Vanguard. Once you get more money to play with, and more investing knowledge, you may want to try out other funds or avenues, but that's usually the consensus for the best places to start.