From memory here. What runway are you using in AKL?
1. The King Air Autopilot Appr mode I believe is only to be used for ILS approaches (Happy to be corrected here as on the 1900 we use the Appr mode as it's more accurate, but that's a different story)
2. Use Nav mode and Alt until you reach the IAF, and be there at the appropriate altitude.
http://aip.net.nz/pdf/NZAA_45.1_45.2.pdf These may not be 100% accurate with what FS uses but it should give a generic reference. EMRAG/LENGU at 3000ft is what we aim for at work.
3. Once you reach profile intercept then descend using the v/s mode. To work out the required v/s theres many formula's that you can use but this is the one that I got taught when I did my initial instrument rating and still works now. Find the ground speed, ie 140kts, divide by 2, = 70 then add a 0 to the end gives 700ft/min decent rate.
4. Use the check heights as you descend and adjust the ROD if necessary.
A bit over the place but hopefully you get the general idea.