tensors22288- Often, getting rid of the rust so that it doesn't come back is easier said than done. Look up a company called Eastwood (sorry, no link handy). They sell everything you need to do this sort of job right the first time.
No, the stuff you use to clean these areas won't damage surrounding components.
Wear safety glasses if you use a wire brush, you don't want to catch a piece of it in the eye and it *will* shed some bristles.
Pulling off wheels won't affect anything like the alignment because the alignment is determined by adjustments to suspension/steering components and is not related to the wheels. Better to ask than to do/not do something that seems intuitively obvious and then regret it
If your wheels/tires are the same size front and back, this might also be a good time to rotate them. Just a thought.
While you have it jacked up and the wheel(s) pulled off, put a jackstand under the frame (or a hefty suspension component) just in case the jack craps out at an inopoortune time. This is also a good time to look around and see if anything looks amiss. Even if you don't really know/understand what you're looking at, stuff like torn pieces of rubber or other obvious problems could be worth noting. At least you'll know that something needs attended to.