King autopilot and GPS approaches

I went and did some LNAV/VNAV approaches yesterday with a King KFC 200
autopilot. Looking for some tips with these autopilots on GPS approaches.

1. In NAV or APP mode the commanded rate of turn appears slower than in
HEADING mode. Spinning the HSI to the desired heading (often 90 degree
turns) caused the plane to try to go in the wrong direction, or the rate of
turn (slightly less than standard) caused an overshoot and didn't capture
the new course.

2. If flying in APP mode, and then making a step down in altitude, the AP
would not capture the glideslope (I've noticed this with ILS approaches as
well, even if intercepting the GS from below)

3. Of course, roll steering would be ideal, but barring this, is there a
better way to utilized the autopilot to fly these approaches?

4. Would it be better to fly in heading mode, and then engage approach mode
just prior to the FAF?