Pupils are rendered entirely by a shader. They don't exist on the model, you just tell the shader where the eyeball is.

It's not a recognised game, surprisingly enough. I never added it. Do you know which version of Source it runs on?

It's not a registered game/engine release in the tools. Apparently it's based on Source 2013, which means that it wants DMX encoding 2 and model format 1.

You can enter these values manually, please let me know if they work. I'll add them.

Fixed in 3.2.6

No issues here. Are you looking in the right location? You can open the console window to see exactly which file paths are being written.

Source will ignore bones which don't have any attached geometry. You'll need to create an Armature modifier for your mesh.

This looks like an internal Blender error. Try reinstalling, and if that doesn't help ask on the Blender website.

Create a parent item for all of your objects, then they will all be exported relative to that location. The parent can be anything including an Empty object.

Blender 2.79 hasn't been supported since 2019. You need to update.

There are many "drive" websites that let you upload files and share them. Any of these will do.