Doubt you even need to try the peroxide.

For one thing what are the "centipede type things" you have? Size, color, damage if any?

And when it comes to fungus gnats, pull back on how you water. The simplest thing to do is to allow the soil surface to dry.

But to get a running start on stopping the gnat's life cycle, use Bacillus thuringiensis israelensis (either Mosquito Dunks or the granular form) in the water you give to your plants. Realize that it takes several weeks to stop the life cycle.

And those "unknown yellow round clusters of eggs" may well be Osmocote, a slow-release fertilizer.

The Hydrogen Peroxide solution you can buy, 3 to 5 percent, will not work for that purpose because it is too weak, unless you dumped a whole very large bottle of it on the plants soil and then it would probably kill the plant before it took care of the insects. There are other, much better solutions to soil pest problems. If you could get an H2O2 solution strong enough (30 to 50 percent) to kill soil insects the reaction of that with the organic matter in the potting soil would more likely start a fire.

mizzella, somewhere on the internet I read that 8.0 ounces of white sugar and 8.0 ounces of 3% hydrogen peroxide in one gallon of water is a good insecticidal drench for plants. I have not used it myself but I am ready for the next insect attack.

But do the "problems" mentioned in the post require any treatment? And if they do, what kind of "treatment."

Identification is always the first step in determining whether or not treatment is needed.

Often, the "treatment" is a simple as this:
1. changing cultural conditions (the gnats);
2. handpicking (the centipede type things);
3. or leaving as is (the "unknown yellow round clusters of eggs" which likely aren't eggs at all).

I have a zebra plant in my office that has really bad fungus gnats! I did not find peroxide to work well. I even pulled a few of the little larva out and dumped them in non-diluted peroxide in a glass. All they did was swim around for 10 minutes before I got tired of waiting for them to die and dumped them in the toilet.

The little yellow clusters could very well be ladybug eggs, very beneficial to your garden, especially if you have noticed aphids or gnats previously or recently.