Yes there are loop products that have enhanced backings designed to prevent the fiber from running.
If your tile floor is properly maintained, you can expect it to last 20 years or more. You will greatly enhance the life of your tile floors or walls by using a properly installed cement backer board.
Properly maintained tile walls installed over a cement backer board can also last 20 or more years.
Yes you can as long as you use a product that’s freeze/thaw stable. Keep in mind slip resistance as well