A few random questions...

1. Is there any way to make a selected weapon affect the player's mobility? People who have played Call of Duty will know what I'm talking about.

2. How do you make a weapon have recoil?

3. Are there any flags that can be applied to enemies to make them resistant to a certain weapon/projectile (Like making an Imp resistant to the Shotgun or Rockets)?

4. Can monsters be equipped with armor?

5. Is there a way to make monsters return to a dormant or wandering state after they have not seen the player for a certain amount of time?

6. How do you make a monster follow a specific path or paths?

7. How do you create a zoom function without mapping it to secondary fire?

8. Location damage (Head shots, limb shots, etc.)?

9. Going prone (lying down)?

These questions may seem odd, but I'm going to attempt to make a Wolfenstein-like TC that has some stealth elements.

Sounds like a cool idea! Unfortunately, AFAIK there is no way to do any of those things (with vanilla/chocolate Doom) without modifying the source. However, the good news is that many of those additions would probably be quite easy to add. Have you looked at the source at all? Do you want to make something that will run in vanilla or chocolate doom?

Chocolate doom would be a good one to try and modify:
http://www.chocolate-doom.org/wiki/index.php/Chocolate_Doom

Also, those things may be currently possible in certain doom ports.

I forgot to state that the source port I was thinking about using was GZDoom, due to the fact that it is the only source port that I have any experience using (Which is odd, seeing as I have very little modding experience to begin with). I am also 100% that head shots and weapon recoil were both pulled off in Brutal Doom, but I can't really see how Sergeant_Mark_IV coded them into DECORATE.

I guess another question that I should add is whether or not GZDoom is the proper source port for adding these modifications. It covers most of the basics that I am looking for (free-look, crouching, skyboxes, openGL support, etc.), but is it able utilize these changes I want to make?

Good question! I've only really looked at vanilla/chocolate, legacy, and doomsday. (but just a bit) I would say at first glance, doomsday would be a good way to go. Honestly, the stuff you want is better suited for an engine like quake3/openarena or source, but I'm sure one of the source ports is capable of what you want.

Doomsday is pretty cool because some folks made 3d models for the monsters, which might be good for location damage. Check out jHRP for that.

I have heard that adding location damage involves modifying the monster's hitbox. The question is... how?