Yes it is possible. You just have to make sure it's on tight! I find rotafixing works very well:
http://en.wikipedia.org/wiki/Rotafix
Once you get your freewheel removed (your LBS can do this if you don't have the proper tool) you can just thread on the cog of your choice. If your chainline is not straight, you will need to rearrange the spacers on your axle. You seemed a little confused on the whole sprocket/spacer thing so I'll try and explain that. Your axle is separate and doesn't have anything to do with your freewheel/cog. Once you remove your freewheel you'll see this. The axle has spacers on it that can be moved around. Once you move them around to get your chainline correct you will have to have a bike shop re-dish your wheel so it's still centered in the frame.
So to answer your questions:
1. No, you don't need additional spacers (unless you can't rearrange them enough to straighten your chain.)
2. Any washer that fits around your axle will work fine. They don't need to be bike specific.
3. Buying a track cog is the easiest way to go. Make sure it has the correct teeth for the chain you'll be using! It must be right-hand threaded.
4. Your hub probably won't have enough threads for the lock ring. But if it does, it will need the same threading as your cog.
5. Yes.