Mr. Danger above is quite familar with the area and gives some good and accurate advice. Here are some of my own additions and suggestions regarding a few of your specific questions:
In terms of Tusayan vs staying at the rim, I would highly recommend trying to get a lodge on the rim. Since you are only staying one night (and doing long drives both coming and going), you are going to want to maximize your time at the canyon. Tusayan is basically a string of tourist-oriented hotels and cafes lining the highway just before the park entrance. Nothing wrong with them, but it not a very pretty or interesting area and it is still a good 15-20 minute drive until you get the rim. If you stay at the rim, than you will really feel like you are at the canyon and can just pop out of your room to the rim to catch a sunset or have a quick walk before dinner any time you want.
While it is true that they frequently get cancellations at the last minute (especially in winter), I would recommend trying to get something reserved ahead of time so that you don't have to worry about it. If there is nothing available online, try calling them directly as last minute cancellations sometimes take a while to show up in the online system.
As far as weather goes, as Mr. Danger notes, the South Rim is at 7,000 feet elevation (2,330 meters) which means it is higher than Denver and has a real winter including snow storms and sub-freezing temps. Northern Arizona winter weather is hard to predict (especially the last few years which have tended to be drier and warmer). In Feb, it might be completely dry and clear with temps in the low 50s or there might be a foot of snow on the ground, ice on the roads and a full storm in progress. Better to dress for the later and hope for the former. Fortunately, even when big storms do occur they tend to be short-lived and roads get cleared off quick.
A couple of notes on routes... the most direct route from Sedona and Oak Creek to Flagstaff and the canyon is up the backend of Oak Creek canyon along 89A. This is a very beautiful and interesting drive, but also very winding and steep - can be a little intimidating for flatland drivers in good weather and scary for everybody in bad. If the weather is looking bad or roads are icy, you probably want to backtrack from Sedona along AZ179 and go up to Flagstaff on I-17 instead.
As far as Flagstaff to the Grand Canyon goes, going up 89A to Cameron and accessing the park via the less-used East Entrance is a more interesting drive and takes you past some nice and less crowded overlooks in the eastern park, but it will also more than an hour to your drive to the lodges or Tusayan compared to going straight from Flagstaff to the canyon along US180 and AZ64 (more so if weather is bad or roads are icy). Given your short time at the canyon and long drives coming and going, you may want to make a beeline to Grand Canyon Village so you can enjoy walking around and being there without feeling more rushed than you already will.
Lastly, since you are going to be in Tucson for a bit, be sure and check out the Sonoran Desert Museum - a world class combination of zoo, botantical garden and museum (west side of town).
Have fun! Its sounds like you have planned a great trip.
Life-long Arizona resident and frequent Grand Canyon visitor and hiker. Live in Phoenix, but grew up in Flagstaff (near Sedona and the canyon) and went to school in Tucson.
My own non-commerical website with recommendations regarding frquently asked questions about visiting the canyon (also pictures and stories from canyon hikes and other places):
Xanterra Reservations Website (Xanterra runs all the lodges at the South Rim):
Arizona Sonoran Desert Museum: