Blender 2.79 hasn't been supported for six years. You can download an older version of the Source Tools if you really want to use it: http://steamreview.org/BlenderSourceTools/archives/

This probably means a corrupt DMX in which the mesh uses more bones than it claims to.

You need to create Source materials yourself. Only material names are exported from Blender.

The button is only disabled if there is nothing in the scene to export. What does your Outliner look like?

I pushed a new commit which adds support for 8 bit and 64 bit integer values.

This doesn't affect model import/export so I won't create a new release of the tools.

Fixed in 3.3.2

No, that's entirely different.

If it works in HLMV then the export was correct. Perhaps the game simply doesn't support this feature.

A corrective shape keys is one with a name consisting of the names of two ore more OTHER shape keys, separated by underscores.

Smile
Frown
Smile_Frown <- this is a corrective shape key

This will be fixed in the next release. For now, you can work around the issue by increasing the DMX binary version to at least 4.