1. You should check your ArmA controls. Zoom in and zoom out is in the game. You find it under "View" as "Zoom in (continuous)" and "Zoom out (continuous)" I'm using dev version. For me it looks in your video like you are using the normal zoom in and zoom out command.

2. Yes I have this, too.

But because of the leaning problem you described in your video you should check the position of your TrackIR camera and the position of your clip. If you zoom in and you loose your centered position you should try to change the camera position or/and your clip position.
You should also check your TrackIR profile settings. Try it with deadzones. Maybe this helps you but also for me it isn't possible to have everything perfect because to high deadzones makes leaning uncomfortable. But saying sth. isn't working correctly while it is working as it should also isn't right.

In development build (Beta under steam) I get entries for the old analog zoom. Now it's named "Zoom in (continuous)" and "Zoom out (continuous)".

But isn't the "Head Forward (Anlg)" function sth. different from the zoom function? More like lean forward. So that it is sth. from Take on Helicopters?

In development build (Beta under steam) I get entries for the old analog zoom. Now it's named "Zoom in (continuous)" and "Zoom out (continuous)".

My Track IR 5 is working well.
Easiest way is to have Track IR hardware connected to your PC and the software running before ArmA is started.
If Track IR isn't active go in your ArmA controls. Then it should be activated. If not go under controls on controller and enable Track IR.