ambient noise (1 Viewer)

1. I can't really comment on.

2. Newer vehicles are more difficult to modify since they tend to use integrated solutions. Older vehicles should not have that problem.

3. Yes, there are aftermarket solutions for reducing the level of road and engine noise, through the use of sound-deadening/vibration-dampening products. One such particular product is Dynamat.

Of your $500, I think it might break down like this:
$100 for the installation of everything
$100 for a bit of sound deadening
$300 for everything else

Of the cars you listed, your best bets in terms of fit and finish are going to be the japanese makers - specifically the Civic and the Corolla. Those two cars will most likely have the highest quality interior parts and thus the least amount of rattles, creaks, and squeaks. I'm not sure how a five or six year old Impreza stacks up, but the newer Imprezas that I've been in have been really terrible as far as ambient noise goes - rattles, wind noise, road noise, etc.

Other than that, I can personally vouch for the Ford Taurus, Ford Escort, Pontiac Sunfire, Pontiac Grand Am, and Chevy Cavalier as all being incredibly poor for interior fit and finish. Road and wind noise are bad, but it's the rattles in these cars that will get you. I can't comment on the Prizm or Stratus without speculating, though.

I own a '99 Subaru Impreza RS and it is very loud inside. You will need to dynamat the entire interior.

So, I would strike that one off the list, although it is a very fun car to drive.

Toyota Corolla
Honda Civic
Pontiac Sunfire
Dodge Stratus
Pontiac Grand Am
Chevrolet Cavalier

any of the above are good choices.

2. Are car radios fully interchangeable? I think I'll want one with AM, FM, CD (plays R/RW) and MP3-CD and ability to add XM and/or Sirius would be nice

DIN is the standard size, and fairly universal.
Alpine's CDA-8911, 9813, and 9815 are fantastic units with all of your listed features. I just bought the 9813 myself.
You'll want a fit-kit for your vehicle of choice that adapts the opening to an aftermarket radio, and wiring harnesses to avoid any wire cutting.

Any general recommendations (up to $200 for HU)?

Alpine or Eclipse ideally. Clarion as a close third.

3. Are there aftermarket steps that can be taken to reduce ambient noise?

yes. dynamat or similar products which reduce metal resonation.

you may want to lok at the Alpine CDA-9813 with the Vdrive amplifier built in. this will save the need for an external amp for your components and provide clean power (27W x 4 RMS)
then look at CDT for fronts and rears (www.thezeb.com)
for classical and jazz, consider perhaps an 8" self amplified sub for low end fill.. it won't shake the car or anything but it will help that lack of low end suffered by most factory systems. the Infinity BassLink sub is a good choice and the 9813 has 3 sets of pre-outs as well, one of which is for subs, so that can go straight to the BassLink.
the 9813 also has a built in 2 or 3 way crossover, and 5 band parametric EQ.
very very helpful to shape the sound to how you want it.
I got mine from etronics.com for $285. far better than Crutchfield's $399 pricetag.