Stefan,
I'm not an expert at it, but I will try to answer some of your questions, sure my answers might be wrong, but I'm going to try anyway...
The evaporator is for the AC system, not the heat. So yes theres a difference...
Do everything you can while it's apart, seal's and all. After you get it all back together, you will be really happy if you don't have to pull it all back apart again next weekend to replace one more doohickey...
Yes you have to remove the whole dash on the 82's. Thats what I have been told anyway...
And #4. You can pressure check it yourself, get a 5 gallon bucket, fill it with water, make an air hose connection to one end of the new core, and it's REAL IMPORTANT to only pressure check with about 20 to 25 pounds of air pressure, (NOT 100 pounds)...
Maybe a picture is worth 1000 words...
And no don't have to refill the AC system, if it hasn't worked in years, and you don't need it to work, then leave it empty. Just refilling it won't do any good unless you replace the parts that are leaking, or are broken then vacuum it down before hand anyway...
No sense going fast--clean/paint/restore each part as you pull it out--that way you trade PITA for a grand accomplishment.
A few quick tips:
1. Make sure your new core is leak free before you install it.
2. By a new gasket kit and use it.
3. Make sure all the vacuum diaphragms work before putting everything back together.
4. There are four bolts through the firewall. Three are removed from the inside;the fourth (upper driver's) is a stud with a nut that must be removed from the engine compartment.
5. The inlet/outlet tubes are a very tight fit through the hole in the firewall, especially if you don't remove the gasket first (gasket best seen/removed from under the car).
Paragon has 2 versions of the heater core for a good price, the more expensive one is the GM OEM one, it's worth the extra bucks to get it for fit and quality.
http://www.corvette-paragon.com/catalog/default.aspx?key=heater+core&part=
Or, I've been told to go with Dr. Rebuild, he has all the parts, as well as a real good diagram of the whole operation, with instructions...