Here's my best in order.
1. Sand the cupping out. Learn to appreciate the built in alarm system you have in your creaking wood stairs... it adds a bit of character. These staircases can be notorious for noise IMHO. Unless you find a contractor to completely rebuilt and guarantee a noiseless staircase, you need to become accustomed to the character of an older home.
2. Not sure if that is the best idea. If you are replacing carpeted stairs the carpet and pad thickness is about 3/4" so there is little difference. If you are replacing treads on a wooden staircase you should probably consider removing and replacing the treads.
3. This will depend upon how your staircase is specifically built. There are many ways the staircases can be constructed.
4. No idea, I am in WA.
GL...