Rans Enduro Sport, Hase Kettweisel Tandem, Merin Bear Valley beater bike
1. I think that it's still possible to buy new 7-speed Sora brake/shift levers.
2. Measure the distance between the rear dropouts. If it's 130mm, then it's possible to upgrade the bike to 8,9,10 speed. If it's 126mm, forget it.
3. Rear derailleur cage length determines how much chain slack it will wrap up. The quick/dirty answer is that triple cranksets need a long cage, double cranksets don't.
4. What teeth range gives the best ride? I think that's a question that only you can answer. Basically, you need a gear low enough to get yourself up the biggest hill that you climb.