Day 2 - train arrives in Greymouth middle of the day. By the time you reach Franz Josef Glacier it will be getting dark with windy hilly roads in twilight, and with no real time for stops along the way (nice places en route include quaint towns at Ross/Harihari/Whataroa, a few lakes, Hokitika for greenstones). Fox Glacier is a bit further down the road.
Day 3 - seeing one of the glaciers will take most or all of the morning. A trip to Lake Matheson & the lagoon if weather is good is well worthwhile. The drive to Wanaka is mostly windy and hilly roads so again will be dark by the time arrive there.
Day 4 - shortest and easiest day of travel.
Milford day trip. Takes a very long day from Queenstown. Not quite so bad from Te Anau but you'll need to leave early to beat the buses. Note at this time of year there is a risk of the road (between Te Anau and Milford) being closed due to snow or avalanches.
Day 7 - not recommended. Whether flying or boating to Stewart Island (weather permitting) you'll need to allow a full day - ie no drive back to Queenstown.
Day 8 - a tiring drive that is deceptively long (travel times on the site you linked exclude the drive from Twizel to Mt Cook village which adds another hour each direction), and you'll be driving into the sun alongside lake Pukaki.
Day 9 - half day drive not counting stops, fairly easy but will have the most traffic. I'm not sure CHC has many flights to SYD in the evening.
b) depends on your itinerary, so for example adding another day on the west coast you could stop first night at a B&B/pub say at Harihari or Whataroa (or Franz Josef), 2nd night at Haast.
c) Wanaka to Mt Cook then to Queenstown makes no sense. A huge amount of backtracking. If you're happy skipping Mt Cook then another option is to fly to Queenstown (either from SYD or from CHC), day trip to Milford and then head north to Christchurch via the West Coast. Doesn't save a lot of time - unless you land in SYD early in the day you'll take another day flying, but does mean a lot less driving and thus a bit less tiring.