I've had to use fire extinguishers twice, and both times it feels like you're using a water pistol to put out a campfire.

I posted my most recent experience here

http://forums.equipped.org/ubbthreads.php?ubb=showflat&Number=215409&page=2

Personally, I'd get a bigger extinguisher. Unless you're the one who started the fire, by the time you get to it it'll be too much to handle for a 2lb extinguisher. Even a 5lb one won't do much. They're great to be able to get people out of danger, but after that you'll just be watching your car burn because they don't last long. I just went out and bought a 20lb air pressurized water and plan on adding some of this stuff
http://www.coldfireextinguisher.com/
I think there are other similar products that do the same thing. One of the things I found out recently was the dry chemical ones do not work well on flammable liquids. You can spray all you want and the flames will blow away, but as soon as you stop spraying the flames come right back (unless you're able to extinguish the entire fire).

As for your questions, this is my opinion.

1) It probably will damage your car. However, if your car is on fire this will be the least of your concern. You can always clean off the powder later, you can't clean burned items. Halon/Halotron may be better for sensitive electrical items, but are you willing to spend $200-$400+, and would you be willing to use it on someone else's car? The two times I've used an extinguisher have been for other people's property, and at least with a cheap extinguisher I don't even hesitate to use it. If i had a Halon one I'd probably use it, but the cost would hurt a lot more to replace it compared to a $10 one.

2) I wouldn't rely on a plastic bracket to hold it, they're basically designed to hold it on a wall. They make metal brackets which are better, but still meant for wall mount. I'm working on making a mount for mine which will use this basic idea.

http://polyperformance.com/shop/Poly-Performance-Quick-Release-Fire-Extinguisher-Mount-p-20655.html

3) What kind of car? I used to have one mounted on my roll bar with a metal bracket, but that was the one I used up last month. In a SUV or wagon I have it under the seat, I haven't mounted it yet.

I'm not a firefighter so take my opinion with a grain of salt. Even the biggest extinguisher isn't going to put out a fully involved car fire, leave that to the fire department. But the worst feeling is seeing a fire start out small and not being able to do anything to prevent it from getting bigger and bigger.