This has been fixed in version 2.4.

Yes, Ctrl+J is join. It's odd that it can't find the eye white textures in that case. Are they still there in Blender? And do they have the same name?

The order doesn't matter, as materials files aren't themselves a part of the build process.

I just noticed that the textures etc. in this image[gyazo.com] aren't in the game's content directory. They should be at SteamApps/Team Fortress 2/tf/materials/models/weapons/c_models/slicker.

The fact that the two move together doesn't mean anything. You need to do one of two things:

1. Run the Join operator on both meshes, resulting in one object.
2. Group the two objects together, resulting in one Source Tools exportable. You can check this from Scene Properies > Source Exportables.

Option two is the best.

You still haven't followed the instructions I linked to. Here they are again.[windows.microsoft.com]

Textured view uses a different rendering path from full-on renders.

Follow the instructions in the link I posted.

File extensions are being hidden in Explorer. You don't have a file called "the_slicker-phys.vmt", you have one called "the_slicker-phys.vmt.vmt".

http://windows.microsoft.com/en-gb/windows/show-hide-file-name-extensions#show-hide-file-name-extensions=windows-7

It clearly isn't, or you wouldn't be seeing the error. :) HLMV will give you the complete path to every material it expects in the bottom-left of the Model tab, labelled "Materials used".

cd is short for "change directory". The QC provides the folder, the DMX/SMD provides the filename.

The error suggests that you're exporting the hat on its own. You'll need to group it with Alyx in Blender so export puts both of them in the same file.