System/casing fan....

I think the worst case scenario would be having the fan burn down and act as a short, you could probably burn your power supply, but this is veeeeeery unlikely, and I can't stress enough how unlikely that is. All you need to do is attach the fan to where ever it goes inside the case, plug it to a 12v connector coming from the power supply and that's it. Those kind of fans consume very little current and your PSU has probably more than enough to handle it.

If the fan runs quietly and smoothly, then it is very likely good. The blades should be clean and should turn without any resistance at any point and without any noise from the bearings when spun with a finger. If you hear the slightest noise or encounter ANY slight resistance when turning the blades slowly by hand, then you should NOT use that fan: it is on its way out, even though it may seem to work satisfactorily for a while. There is no essential difference between a case fan and a power supply fan so if the marked voltage is correct, the connections are compatible and the wires long enough, they should be interchangeable. Some fans, especially those which cool the CPU or graphics chip, are designed to run at variable speeds and they usually have four connections rather than three. As long as the connector fits the socket (and the fan fits the case), you can generally assume that they are compatible.

Not sure what you mean here. Sounds like you want extra cooling for the case because any working power supply box I think comes complete with fan. I see no reason you can not use any 12v fan terminal on board to power an additional fan as any cpu fan will. Sure we know that electric motors can grow old and suck up the juice but unlikely I think, fans do get noisy with age, if your power supply is sufficient there shouldn't be an issue for running it. If there is and your power supply can not handle an extra fan you will get negative performance from your board and you won't like that. I think this accurate info but curious to hear what any computer enthusiasts might say about this question, surfer.