1. Yes but if your new fan is too quite (low CFM) you may run into problems with cooling since most good PSUs have thermally controlled fans. And I wouldn't snip the wires, if you have a nice PSU you can pull out the connecter and figure out a way to use a 3 pin or just end up snipping and splicing. Just make sure your splicing goes well and it won't just up and stop working on you.
2. Not unless you mess up, but it will void the warentee.
3. With modern day, high quality PSUs powering high quality systems, yes. Unless you have a lot of air being pushed out of your case and no were else for it to go out... You don't need a ton of airflow really, PSUs can get hot and still work, however when they do get too hot their voltages start to get unstable and drop. Essentially, yes.
4. Ya, if you put a Potentiometer in there or hook the fan up to a Baybus of sorts.