Does downloading most fps games slow down your computer

Not necessarily. It depends on how many you are trying to download. I assume by 'fps' you mean first person shooter, and in this case if you were to download quite a lot, yes. It will clutter up your hard drive and cause countless registry errors. However, if you have a fairly substantial hard drive (at least 180GB) then you are unlikely to encounter many issues. A free registry cleaner such as Eusing Free Registry Cleaner can clean up many missing or invalid entries, but then again you should check how much memory and graphics capacity is required to play your game.