Just guessing until the files arrive, but if you change the reference mesh's skeleton you'll also need to export all of your animations again.

You have over-complicated things and confused yourself again.

You are animating a mesh called called "animatedentity_animation", but on QC line 5 give studiomdl a completely unrelated mesh called "animatedentity". This mesh isn't linked to any armatures, so cannot animate. You should change line 5 to:
You can delete all the other meshes from your scene. The same SMD file can be used for $collisionmodel and the and idle $sequence. (I would suggest removing the $collisionmodel line until you have the basics working though, as it has special requirements.)

In the video you introduce another error to your QC file when you change line 13 from "anims/ArmatureAction.002.smd" to "animatedentity_animation.smd". The latter file contains a mesh with no animation, so change it back.

You're trying to use delta animation, which is an advanced feature intended for complicated organic models. For your purposes just defne the animation in the same way as you do the idle animation. Then in HLMV, instead of clicking the radio button change the first drop-down from "idle" to "animation".

The guy on Facepunch is correct. Source only supports skeletal animation, and on top of that can't scale bones.

If you want motion like this you can export a vertex animation, but that's very costly and shouldn't normally be done. See the Scene Properties tab in Blender for help on that.

So binary 6 / model 15 works?

It's impossible to say without having the files you're importing. VTA is a bit of a crap format which relies on positions matching the original SMD though, so it's quite possible that it's broken.

No idea, ask on a TF2 forum.

That's correct, there is no Linux SDK. You can still import/export your models, you'll just need to get someone with Windows to compile them. Not sure if it'll work though emulation as the tools all talk to Steam.

The difference might be down to Blender using horizontal FOV and Source using vertical FOV (or vice versa).

I've had a brief look and it appears to be a precision issue in Blender. It's tricky to just say "there's no keyframe so don't move it" as you can have things like bone modifiers or constraints the effects of which need to be baked out. I'll dig a bit more.