NavList:

Ed
Forgive me if I answer this bit by bit, maybe not in the order you asked. 
1.  You don’t really need to know exactly what goes on inside the Kollsman mount.  You just need to know what works for you.  Otherwise, probably half the Navigators who ever used one would have been up the creek without a paddle. 

2.  I’ve not really worked out the geometry until now, but you’ve goaded me into it.  It’s not too different from a Smiths Kelvin Hughes sextant.  You simply end up with the angle between the nose of the aircraft and the way the sextant is pointing as the difference between aircraft heading and the stars azimuth.

3.  There’s only one rose/disc.  The set heading knob is geared onto it.  If you look at the bottom of the mounting, there’s a window showing a portion of the azimuth disc and a little arrow pointing towards the disc.  If you wind the set heading knob until 000.0 appears in the heading window on the mounting, the little arrow on the mounting will be pointing towards N on the disc. 

4. Look behind the set heading facility and you’ll find a little lever.  You can use that lever to lock the sextant to the azimuth disc, and then the only way you can move the sextant in its mounting is by turning the set heading knob.  Note also that the numbers on the disc increase anticlockwise to allow for the fact that in service the face of the disc points downwards.  The mounting is also fitted to the aircraft such that if 000.0 is set in the set heading window, N on the disc points towards the tail.  This is to allow for the fact that the azimuth disc viewing window in the sextant is on the rear of the sextant while the index mirror window points forwards.

5. So, assuming your mounting is fitted in the aircraft correctly, i.e. With 000.0 set in the heading window, the centre of the fin corresponds with an azimuth of 180, you find your star as follows.  Set the aircraft heading in the set heading window.  Set Hc on the sextant.  Swing the sextant until the star’s azimuth appears on the azimuth disc visible though the eyepiece.  And there will be your star (plus 3 or 4 dimmer ones, but the pictures in the Air Almanac tell you which is yours).

6. To do a heading check in this situation. Move the sextant until the star’s exact azimuth is on the azimuth disc.  Flick the locking switch to the lock the sextant to the azimuth disc.  Wind the set heading knob until the star is back in the cross hairs.  You true heading is now set in the heading window.   

7.  If this isn’t enough, I’ll go through your additional questions and assumptions, but I think the above covers most of it.  DaveP