If the game you are wanting to copy is one you bought from the PlayStation Store, you have no worries. You can just re-download it from the download list in the PlayStation Store once you get the replacement system up and running. The main things you will want to back up are your game saves as well as any game info, videos, music, etc. you have on there.
That in part answers your second question- yes, you can use your current PSN ID. When you set up the master account and go to the "sign up for the PlayStation network" icon, just select "use an existing log in" and put in your e-mail and password.