1 I use a Nexus 7, which may be more utility-oriented than the Alfine. No problems, ever, with the exception of cable icing, which is easily prevented doing what tsl does.
2 Marathon Winter plus Mr. Tuffy gives the same rate of flats per mile as the tires on my car. I don't carry anything for fixing flats. If I got one, I'd hail a cab.
3 I've had the bike for 16 years, so any Shimano warranty has long expired. I will say that towing a trailer, standing on the pedals, and cold weather have been SOP for years. No problem.
I did ride with a derailleur for one winter. It was a bit like using a violin to hammer nails.