I'll take a shot, but I've only been here in ft collins for about a year now...
1. Depends on the size of the lot as that factors in as well - my guess on say a 3bd/2bath with around 2000-2500 sq feet total about $1500-1700. It will vary but prop taxes are not that bad.
2. Yes many do - of course some dont. BUT its easy to find a house with a basement if you need one. You will find that in the case of homes with 2500-3000 sq feet that 1/2 of that is below grade in the basement. Maybe only 1500 or so above grade. Of course it depends, but in that price range that is a pretty fair guess. I am personally shopping in the 230 and under price range in mostly the older areas on the central/west side so that has been my experience
3. Depends on your usage

I lived in a 2300 sq foot home (rental) that was 1200 up and 1100 basement. It had a 25 year old furnace and I kept my temp at about 65 in the winter. My bill was usually around $120-130 per month for gas (which also included my hot water heater which was gas as well). I imagine if my furnace was more efficient (and not past the end of its life

), I would have done even better. Most heat is natural gas not propane unless you live outside the city limits where there are no city utils. In that case you are probably looking at a propane tank in your yard and a higher cost for fuel than natural gas.
4. Yep - no problems there. As long as you are within the city limits you should be OK. AND I'm willing to bet that just outside the city you are fine as well - you just may not have as many choices (might get DSL only instead of cable and DSL). I have comcast cable (live in the city) and it is very fast and very reliable (8Mbit down /1Mbit up for about $50). I've only been offline for maybe 1 or 2 times in the past year and it lasted no more than 5 minutes.
5. Don't think its an issue in Ft Collins if you are within the city. Outside the city with new construction (outside an established development), maybe. I have no exp. there.
6. IMO the school system is quite good (excellent?). There are many excellent elementary schools in the Poudre district.
Good luck.