Popping sounds are generally either a sound from a spark, or a failure of an electronic component. They do not always mean that something failed. For example, plugging in electronics that use lots of power will often cause a small spark to form when plugging them in. As an example, my Lenovo laptop power adapter will often make a sparking noise when I plug it into an outlet and it is not a cause for concern.
Does your power adapter create such a noise when using other outlets? If so, then you may not need to worry at all. See this question for some more details on this transient arcing.
But, sometimes noises do indicate failures, for example when a capacitor, MOV or IC explodes. You could also hear a click when a circuit breaker trips, but this would cause a circuit in your house to be no longer be energized. Some power bars also have internal circuit breakers, which can also make a click when they trip.
In your case, I'd first say that a used surge suppressor probably may not provide much protection for your electronics. If you are concerned about surges, you should look into verifying that your house has a good ground, installing a whole-house surge suppressor, using quality surge suppressors where your electronics are installed on both the power lines and data lines such as telephone or CATV. Surge suppressors do age, and can only handle a certain amount of surge during their lifetime. Ensure that new surge suppressors meet the new UL standard 1449 v3 by checking for a holographic sticker that says "Surge Protection Device".
Now to your other questions:
2) This should be safe. Any over currents should be protected by your house's circuit breakers, and a lamp is a pretty "robust" device that wouldn't be seriously damaged by a bad power supply (though the bulb may burn out). That said, do this in an area where if the power strip catches fire, it won't damage anything, and you could quickly pull the plug out of the wall socket if something bad happens. Don't put water on an electrical fire.
3) As I said above, the power bar may not provide significant surge protection, especially now that it may have failed. You may want to dismantle it (while it is unplugged) and see if there are any burnt/charred/damaged components.
This answer is more of a matter of opinion. To be safest, you could replace it with a high quality surge suppressor, but with some investigation, it is likely as safe to use as any other power bar.
Unless I'm missing something, this is allowed, provided you have enough room in the boxes for the number of conductors coming through and connecting within. If not, you may need a larger junction box. For a continuous 20A load, you would need a separate line, but in this case, you are simply attaching a device with a 20A plug that itself provides multiple outlets (not a continuous load).
Since your pool lamp could potentially short or cause other issues (it being near water, etc.), you should consider moving it to another circuit so that you don't risk tripping the breaker on your computer equipment.
Best Answer
This could be a bunch of problems, from a missing ground to a voltage spike, to dying speakers, etc...
First of all, it would be helpful to rule in/out the computer as the source of the popping. It's possible your computer's sound card is not great and is sending those noises to the speaker, which is faithfully playing them. Try plugging the speakers into a different device (e.g. an iPod), AT THE SAME OUTLET. Then see if you get the popping noises.
If you still do, try moving the speakers to a different outlet somewhere else in the house. Event though the light switch doesn't control the computer's outlet, they could still be on the same circuit and causing some other kind of interference.
If moving the speakers to a different outlet solves the problem, there may be issue with the wiring. (Could be the switch is bad and is causing a ground fault or something. Or maybe the unused switched outlets are bad. Or something else.)
As @Tester101 says in his comment, problems with the ground can cause audio issues. Do the speakers have a ground pin (3rd prong), and if so, is the outlet properly grounded? You can also get so-called "ground loops" when different components have different grounds, which can cause a voltage difference—are the computer and speakers plugged into different outlets?
An outlet tester is an easy and safe way to do quick sanity checks on outlet wiring. You just plug it into an outlet and the lights will tell you if there are some common wiring problems. If I were you I would pick one up and test all of the outlets, including the unused switched ones.