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You can deadhead the flower stems back to the base of the plant.
Though it would clean up the garden to remove the stems, it's best to let them die back naturally. Continue to water, to prevent them drying up to quickly.

It may be excess nitrogen in the soil from over fertilizing.
You can use a phosphorous addition, such as Bone Meal to promote flowering.
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/bone-meal-fertilizer.htm

Deadhead at the base of the flower. They can be gently snapped off or a small garden scissors used.

These are seed heads. You want to remove them. Cut the stem down to the base of the plant. When you new flowers become spent remove them. When the cluster of flowers is finished cut the stem off at the base. This will help encourage the plant to form new stems and flowers. By leaving the seed heads on the plant spends energy on developing mature seeds instead of reblooming.

This will depend on your weather and temperatures.
Daylilies benefit more from deep watering, which reaches 8 to 10 inches into the soil, than from a succession of brief, surface waterings.

A soil test would tell you if you have excess nitrogen in the soil. Bone Meal is a good way to boost phosphorous; which should promote flowering.

Also after flowering it is a good idea to remove any seed pods that form. Leaving them on the plant can retard next years blooms.

https://www.gardeningknowhow.com/ornamental/bulbs/daylily/growing-daylilies.htm