With fast startup enabled, the file systems are copied onto RAM and remain there in a pseudo sleep mode; in this state your computer is in a suspended state with no background activity; so to answer your question, "Does this mean the computer is still doing stuff even though I clicked shut-down?" No, your computer is not doing any stuff after it is shut down. As far as turn off your power supply, there are no issues as long as you let your PC shutdown completely, usually indicated by your power button light turning off. However, when you turn your power supply off, it may drain your RAM, which will in affect, disable fast startup, which again does no damage, it just means your PC will take a little longer to boot. If your PC does a hard shutdown, without going through the shutdown process, it's always a good idea to unplug your PC and then press the power button. This will drain the remaining power in the PSU that fast startup needs to function, and clear out the RAM of what may be corrupt data.