1. If I move to another address (aka ip address as well) will there be any issues with logging in?
Not per se. A different internet connection might have its own issues, but the game doesn't care.
2. If I ever had to reformat this computer will my activation code from the retail product work again?
3. If I ever have to replace this computer will my activation code still work?
Strictly the answer is "no", but it's the wrong question. The retail code was to activate your account on Cryptic's servers. That code will only work once, for one account.
You can install the STO client on as many computers as you like; it does not need anything special to install (you'll get a web browser open during the install, inviting you to enter a retail code; you can just close it).
You can login to any STO client on any computer using your account.