First off, welcome to the hobby.
You made a good choice with the car. I'm racing my Pro4 tomorrow, and I can't wait.
I haven't had problem one happen to me, but are you using a chisel tip. It looks like a flathead screwdriver, as opposed to the pencil tip, that definately helps things melt faster.
Problem two: I use foam tape to mount all my eletronics. obviously, you don't need to mount your servo with the tape, because of the mounts. But generally, you need something to separate the electronics from the graphite chassis (which is conductive). Velcro, double sided tape, foam tape, all work. Stay away from glues, such as Shoe Goo. I had glitching problems when I used this.
Problem three... This WILL get frustrating if you don't have a hot, high quality soldering iron. Those little tubes are a pain to get the wire soldered to. You just have to solder the battery wires on any part of the tubes. If you're having trouble, just ask. 99% of us nutty racers are more than willing to help.
Problem four- I'm not familiar with that charger, but the motor run-in sounds nice. If you don't quite know how to work it, either ask, or run the motor with no load (outside of the car) for a few minutes, then look at the brush ends to see if the full brush face is making contact. Most people recommend 2 or 3 minutes at 3 volts. I'd just run it at 1/4 to 1/3 throttle if you run it through your transmitter, for a few minutes. Of course you don't HAVE to run your motor in, you can just slap it in there and throw the car on the track. But your motor will thank you in the long run...
That should cover it, and if you need anything else, ask. Good luck with your race, and don't worry about winning. Just stay off the boards, and you'll have fun.