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Daylilies do not self-sow and clumps slowly increase in size. In fact, the clump will decline and look dead in the center if you don't divide it every 5 years or so. Pachysandra surely spreads but is not aggressive in my experience. One likes sun, the other shade. Daylilies like some fertilizer if they are repeat bloomers; don't fertilize pachy.

I think you are spot on, in all accounts. Everything you have mentioned is correct. here is a link for more information: https://www.gardeningknowhow.com/ornamental/groundcover/pachysandra/pachysandra-ground-cover.htm

Unfortunately, just about anything you spray will unintentionally deter and possibly kill your predatory bugs as well. Here is an article that will explain in more detail:

https://www.gardeningknowhow.com/garden-how-to/beneficial/neem-oil-and-ladybugs.htm

I don't think that this was the issue. It was likely over watered, which led to an infection in the soil. I would treat it with wettable sulfur, and dolomitic lime to recondition it for another plant.

It should only be watered when the soil remains dry for extended periods. This will help keep it from getting an infection in the future.

The soil may have already fostered the infection before you planted, so this may be of not fault of your own. You can treat the soil with the treatment mentioned above, and it will likely rid it of the infection.

This article will give you more information on their care: https://www.gardeningknowhow.com/ornamental/groundcover/pachysandra/

Fertilize with a 12-12-12 NPK.

Water in the fertilizer after spreading under the leaves.

If the plants have filled in you should not have to use mulch.

Pachysandra should be just fine as a ground cover under the shrub.