Good for you for getting out there! Don't get discouraged.
It sucks to get stuff stolen. It's likely to happen again if you're leaving the bike outside at night unfortunately, so try to find a way to bring it in. I'm assuming you didn't have the wheels locked. If you are leaving it locked outside a lot, you need at least one good U-lock to get one wheel and the frame and maybe a decent cable to get the other wheel. There's several ways (and debate about the best way) to lock a bike. Nothing's theft proof, but the better locked, the more likely they'll look for an easier target. You can get special little cables to secure the seat to the frame. Or some people now take a short piece of old bike chain and tie the seat down with it.
Doesn't sound like you're having a good experience at your local shop. Look around for another if possible. Having a good mechanic you trust who will treat you well is very valuable and worth going a little out of your way.
On your gear noise, you need to figure out if this is coming from the front or back, is it in all gears or just some, can you see anything rubbing on the chain, etc. These tutorials are a good place to start:
http://bicycletutor.com/part/derailleur/
In general, you don't need to be a master mechanic to ride a lot. But there are a few things you should learn. How to change a flat tire is #1. You shouldn't get them often, but it sucks to get stranded because you don't know how to change it or have the tool with you. There are a lot of online sites with basic instructions. But nothing beats hands-on. See if you can get someone to walk you through it. And then actually do it at least once on your own. The first time you try shouldn't be on the road and late for work.
Basic bike maintenance is not hard. But it is a little tough to get started if you have no experience and no tools. Don't be afraid to tinker a little. As you learn a little, it will get much easier to learn more.
Depending on where you are, there are more and more groups out there dedicated to helping people learn to handle their bike themselves. Some specifically focus on women since there are more barriers to women feeling comfortable and getting the skills they need. This is a great female run organization in Los Angeles:
http://cicle.org/ You might see if they can refer you to someone in your area.
Keep an eye out for other female cyclists and don't be afraid to stop them and grill them for recommendations on good shops, where they get help, etc. Bikers tend to stick together and love to help each other out.
And get some tires with kevlar belts, you shouldn't be getting so many flats