Electronic – 24V 3A from ATX power supply

Can't make out what the picture is supposed to be of, but the mush you refer to is likely some thermal compound or adhesive.
It's probably one of the inductors or transformers on the board, which can vibrate slightly when passing a switching current. This is called magnetostriction. Capacitors can also buzz but it is more likely to be the magnetics.
It is not an indicator that the power supply is faulty. You can dampen it by making sure the magnetic components are solidly fixed to the PCB (e.g. with the adhesive mentioned above)

I don't advise trying to service it yourself (no need if it's not faulty anyway) but just in case and since you asked: You probably want to wait at least ten minutes (the longer the better) after unplugging the supply, and then make sure no significant charge is left in the large capacitors. Most large caps will have a high value parallel "bleeder" resistor across them so they discharge slowly when power is turned off, but do not rely on one being present and working. Some capacitors can hold a charge for days if no means of discharge is present.
See the section "why this matters" and "discharge technique" on this page for some decent info. Be very cautious, you can receive a lethal shock from a large filter cap, or they can explode or even vaporise metal.

You should be able to find cheap 48V DC power supplies on e.g. ebay. Those are commonly used in industrial applications. Not clear if you are looking for an adjustable power supply or not...

If you have a floating power supply you can also connect them in series (e.g. two 24VDC supplies in series can give you 48V DC). If you have two lower voltage adjustale floating power supplies (most lab ones I've seen are) you can use them in series to get adjustable higher voltage. Shouldn't be too expensive, a quick google shows you can get a 30VDC adjustable supply for less than $100.

Building your own adjustable DC power supply is going to be a bit more complicated. If you go that route by the time you're all done it will cost you more than buying one (though you will learn a lot). Cheapest option is probably a bunch of 9V batteries in series (just don't short them).