I will only have our 1st trip to NZ later this month, but I've been researching a few months from forums, and happen to see that your itinerary is somewhat similar to ours, hence daring myself to share. Our plan:
1N CHC
1N Arthur Pass
1N Hokitika
1N Fox Glacier
2N Wanaka
2N Te Anau
3N QTN
1N Mt Cook (White Horse Hill)
1N Glentanner
1N Geraldine
1N CHC
To some of your questions:
Don't stay overnight in Haast, there's nothing there but sandflies (said people in TripAdvisor forum
5N Cromwell : I'd rather choose 2N Wanaka + 3N Queenstown, to minimize travelling time every day.
Mt Cook : if you're not campervaning, then 1st option for lodging (nearest) should be in Mt Cook Village. 2nd nearest is Glentanner (much closer than Twizel).
As said, I haven't done my trip yet, so take this with a pinch of salt