As you may have guessed, these topics aren't easy to explain by typing on a forum...
1. CivicSpoon is correct about warming up the transmission. You shouldn't be fearful of the increased pressure needed to move the shifter in cold weather. If you had been driving before the advent of modern synthetic lubricants, you would have REALLY been worried! What you think of as being difficult to shift when cold is much, much easier than it used to be!
2. The downshifting thing is also difficult to explain without being able to show you the workings of the transmission. When you down-shift, you're trying to force two gears spinning at different RPMs to mesh in a way that increases the load on the lower gear. That's why rev-matching helps so much... you get the two 'involved' gears spinning at something close to the same speed. Rev-matching is a good thing. It also reduces the load (and thus the wear) on the synchronizers. I rarely downshift without doing it.
3. Do you have any large parking lots in your area that are empty on weekends, in the evenings or at night? When I've taught people to drive, I like to get them into a large, open area where they can concentrate on the mechanical aspects of driving without having to think about other traffic. This is especially helpful when learning winter driving techniques, since you don't have to worry so much about losing control of the car.
The one piece of advice I'd give you that differs from CivicSpoon's is that I like to see drivers 'push the envelope' a little at a time. Learning the safe limits of your car on a parking lot or closed road will make you a more confident driver. I'm not suggesting that you go out and intentionally try to make the car slide - or anything like that. If you have a friend who enjoys driving fast, take him along. Just pushing it a little harder each time you 'practice' almost always makes a big difference in your abilities when driving on the road. SL