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1. - We skipped the Tranzalpine cos we had a car the entire time, so I can't compare, but yes, it is the case, that there is amazing scenery everywhere. The train also locks you into a certian timeframe and itinerary that, with a car, might be more flexible.

2. Again, we did neither, but we did do Franz Josef, for free, We walked up to the glacier terminal and had great views. However, if you actually wish to go on the ice or touch the glacier then yes, you must pay for a tour.

3. In 7 days I can't see how you are fitting all of this in. We had 2 nights in Queenstown, then a night in Te Anau with a glow worm tour, a full day seeing Milford Sound and stopping frequently on the return to see the forests and waterfalls and snow, then another night in Te Anau. To fit in a day kayaking in Milford you will need to be in Te Anau the night before, and either the night after, or have a 5 hour drive back at the end of a long day. 2, you have 2 nights Queenstown, 2 nights te anau, and you are going to see the rest of the south island in 3 nights? Not happening. I would have 1 night in Queenstown, have a big day there, then spend that night in Te Anau. Get an early start, do Milford BUT NOT A FULL DAY, make it a cruise or half day kayaking, then get back to Queenstown that night. Still an insanely busy trip, but at least you have a bit more time. You then have to decide which 1, of the 2 "sides" to do - EITHER from CChurch head over Arthurs Pass and do the glaciers in your remaining 4 days (my pick) OR do Mt Cook. This side is easier and quicker though.

4. Sorry, can't assist here. We stayed in the fabulous NZ caravan parks. Most have very nice cabins at a good price. I honestly don't see how the farmstay fits into this itinerary. The south island is a lot bigger than it looks, the roads are long, slow, scneic and winding. The glaciers to Queenstown for example takes 5 hours. Queenstown to Milford is a 5 hour drive EACH WAY.

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The Tranzalpine is amazing, but it follows the same route as the road except where it dives into a tunnel, and I think that means that you don't see the fantastic Otira viaduct. Of course with the train, someone else drives so all you have to do is admire the scenery.

there's loads to do round Te Anau; Kepler Track, Manapouri walks plus it is nice little town and it gets a lot less rain than the rest of Fiordland. Remember that you don't really need 'activities' - you need doc.govt.nz, some decent walking shoes and a pair of working eyes. :-)

almost everywhere in NZ has unpredictable weather. Have you considered the smaller hostels (bbh.co.nz for prices and reviews). Many of these are memorable in themselves and you usually get a lounge with a stack of books and magazines and other people to talk to if you get a bad weather day.

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I think with your schedule, you'll have to either head south from ChCh, via Tekapo road for views, and end up in Te Anau after a day or three.
or
Drive over Arthurs pass and head down the West Coast via a Glacier, to Te Anau after 2-4 days.