Recommended Tools and Approaches

#1 Games such as Unreal and Quake use BSP files to store their levels. In Torque, these are called interiors. If you've played Tribes, you'll know the deal - the buildings on the terrain are each an interior file, loaded and plonked onto the terrain. To make interiors, you'll ned either Constructor, which you should be able to download free if you have a licence (not sure what happens if you don't), or have a look for a program called QuArK.
Torque isn't really geared to all-indoor maps like those found in the games you mention, but it's simple enough to make a nice big interior as your level and stick it on the terrain. Nobody said you have to have any exits from the interior.

#2 In my game I use the polysoup collision code and Blender. It's a joy to work with. If you like pain, use some other method.

#3 If you want a tip on testing out game rules or balancing, I'd say Excel or that spreadsheet app Google has. Since a lot of game mechanic rules come down to small functions, you can execute many of them as cell formulas in a spread sheet and then use that for testing or to get statistical data. I use it for most of my MORPG's core rules, and then port it over to script or code. It can also help when you want to just see the numbers without the game visuals cluttering things up.

On the art side, Daniel was spot-on with Constructor (it's dedicated to Torque, so there's less chance of encountering issues). You can use poly-soup as well, or mix and match by using DIFs with DTS details mounted on it, or DTS models using transparent DIF collision brushes. I haven't played with poly-soup yet, so I'm more familiar with DIF creation, but unless you have so many interiors that it would decrease performance, poly-soup really does offer much more detailed interiors.

#4 Best advice is to experiment and find the tools that suit you and your project. You'll find situations where one format seems to be more fitting than another despite what anyone else says, and you'll never know unless you try.

But to answer your general question, the Mission Editor is used set up and design the world in general. You'll create your objects and Interiors in other outside programs (the ones that work the best for you), but you'll place them in the world using the in-game editor.