Air powered filter work well, are cheap, use very little electricity but can "leak" by backsiphoning, and tend to be noisy.
Hello; I have had both issues with an air pump and air operated filters. I have solved them in different ways.
There are anti siphon valves that can be used on air lines. These are essentially one way valves so the siphon cannot happen. The more common way I deal with the potential of a siphon is to make a loop of air hose higher than the top of a tank. This breaks the siphon also. At least I have use such a setup for decades with the power going off plenty often.
Air pump noise can be a tough one. The culprit is that the air pumps have a 60 cycle vibration. I have an air pump right now running my QT on a kitchen counter. ( I am a bachelor in my own home so I can do such). I put the sponge base of a sponge filter under it and it is quiet.
Air pumps can be wrapped in sound absorbing stuff but two things need to be kept in mind. One is that the pump needs to be able to draw enough air so the wrap needs to allow for that. Another is the pump does make some heat so the wrap might shorten the life of the pump. I use this method less than any other.
I have hung the air pumps so they do not touch any surfaces. This is the more common method I use. Rubber bands work fine except they eventually give out and break. The small bungee chords last a bit longer.
I sometimes just make a loop in the power chord and hang a pump that way. Not necessarily the quietest but often quiet enough. My current main pump running three tanks is in the basement hanging on it's power chord with a long air line running up thru a hole in the floor. I used some air line of the sort used by folks who are on oxygen tanks. This stuff is a bit more resistant to ballooning so I do not lose air that way. One note if this hose is used being that the inner part of this has little ribs ( I think so is cannot be pinched closed easy). I used a small Dremel tool to remove enough of these ribs so I can use regular aquarium pump fittings.
There likely are other ways to deal with both issues but these are some I have used.