Like this.

That's the render properties for the current scene. Scene properties itself is two tabs to the right.

It is a bit confusing I will admit.

The panel will appear at the very bottom of the Scene Properties tab.

If you're really sure that it isn't there, did you follow all the instructions on the download page to enabled it?

If you did, are there any messages in the console? Use the Window menu to open it.

Can you upload your blend please.

Sensible. I'll give it a shot when I'm next free.

https://developer.valvesoftware.com/wiki/Blender_Source_Tools_Help#Meshes

See "My mesh is in the wrong place". Does that help?

You probably downloaded the file incorrectly. Open it in notepad and see if it matches what's on the web page.

What you're seeing is the skeleton in its rest posiiton. You can reproduce that in Blender by selecting all bones in Pose mode and running the "Clear Post Transforms" operator.

Why the animations are messing up I don't yet know. Have you exported them too, or are you using the decompilled files?

Can you upload your blend file please.

As Zappy suggests, when you applied the modifier you broke the link between the mesh and the armature. The good news is that your bone weights should still be there, so you can just create a new armature modifier, link it to the armature, and export again.