What's your question? Ask

Given the timing of the moss' demise with your pool's blow up floater, I would say that chlorine from your pool water might be to blame for your irish moss turning yellow. It does not seem as though the floater would be heavy enough to damage the moss by sheer weight. The best thing I can recommend is rinsing the moss with clear water from the garden hose to flush out any possible remnants of chlorine.

It's hard to say what the insect is from your description but I would go ahead and treat the Irish Moss with Neem Oil. It acts as both an insecticide and fungicide.

Here is more information.
https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm

Make sure the damaged part's roots are fully in contact with the soil. You may have to move away the mulch and add some new soil underneath to give it an easier time getting established again, while leaving the healthy part in contact with the soil. If the damaged part doesn't recover, you can also propagate Irish moss by division and use the new growth to fill in gaps.

It should be possible to plant Irish moss between perennials, since it is not an aggressive plant and shouldn't overtake them. It is possible, though, that you'll need to weed out the Irish moss growing closest to the flowers if it seems to be impairing their growth- that depends on the flowers you choose and how well they do with crowding.

There is not anything that you have to do to care for these in the winter months. They will survive just about anywhere in the US without help. Anything you do to try and help may actually harm the natural process in this case.

Irish moss does best with morning sun and afternoon shade. If your weather is very hot, this may cause the moss to turn brown despite being moist. It should recover when cooler temps return. Irish moss can turn brown as it ages. If any of these patches are old, trim out the brown sections. https://www.gardeningknowhow.com/ornamental/groundcover/irish-moss/growing-irish-moss-plants.htm