1. Recenter. The normal mode always had me centering the stick too late, adding more input on top of what was trimmed. Kinda annoying in some circumstances.
2. Er, kinda. If altitude hold is engaged, it acts as the "trimmer" for that channel. Keep it pushed while changing altitude, release at new altitude to send that to AP.
3. Route puts you either on course or on track (selectable) to the selected waypoint. The first 5 waypoints created in the editor are automatically programmed into the nav computer. The airfield you take off from is always stored as well.
Descent mode does an auto descent if you keep it pressed, use in combination with hover hold. Keep in mind the AP has limited authority, so if it fails to descend you have too much collective applied for the AP to correct for.
4. Maybe... trim the new heading before enabling the heading hold again though. Note that such a procedure would get you booted out of the airforce (
never turn off hold channels, end of discussion).
Try turning using Shkval and auto-turn instead, perhaps with the HMS to make bigger, instant corrections (as compared to slewing Shkval). I'd only trim a little rudder to not have to adjust AP input to line up Vikhr reticle. Never really tried turning the helo with rudder in a hover; if I'm in a hover I'm setting up an attack, in which case I have the auto-turn enabled.
And again:
http://www.subsim.com/radioroom/showthread.php?t=170158
It seriously answers most of those questions in far more detail.
