Any tips for making the cars less mad at you? (or maybe caring less?)
If you're cycling sensibly (don't weave all over the road, don't be overly aggressive, signal your lane changes well in advance, use lights and reflectors at night, stop at traffic lights/stop signs, etc.), most drivers are going to be pretty reasonable. You'll always get a few folks who are having a bad day and see you as a vulnerable person that they can take out their problems on. Honestly, there's not too much that you can do beyond taking a moment to try and figure out if maybe you did something that triggered their anger, and then letting it go.
People are beeping at me
Some people will go behind you and honk because they incorrectly believe that this is safer (by letting you know that they are there before they pass I guess?). Not much you can do about this, beyond keep your cool and just ignore it.
overtaking me without moving fully into the other lane
You can try cycling further towards the middle of the lane, rather than staying as far to the right as possible. There's some kind of psychological thing that goes on that makes a person driving really, really, really, not want to cross over the line into the next lane. Often if you're cycling really far to the right, cars will pass you very closely in order to stay in the same lane as you. When you ride a foot or two from the right you get more room to maneuver around obstacles (potholes/debris), but more importantly, it forces a car to cross that line and exit the lane in order to pass you. Most cars don't care about close passing a cyclist, but are loathe to put a cyclist sized dent in their vehicle. :P
almost want to get a shirt with this logo or stick it to my backpack or something
Unfortunately, the kind of person who is a dick to a cyclist isn't likely to change their behaviour by reading something on a cyclists back.
Question: Do you have a video camera (like a dashcam) on your bike in case of accidents? If I get smooshed I feel like my parents will want to know who did it...
Nope. I don't think there's any real utility in having a camera while cycling. Having a record of the accident doesn't prevent the accident, which is what you really want.