Answer: Daylilies bloom over a short time and each flower lasts a day. You can snap off each bloom when it is faded and then when all of the flowers on a tall stem or scape have faded the scape itself can be removed. Cut it off at the base down near the ground. If the plant is going to bloom again it will send up another scape. Some (most) varieties produce scapes to bloom over a week or two once a year, while reblooming varieties will rebloom one or more times in a season if conditions are favorable. The deadheading serves to conserve the plant's energy by preventing it from setting seed. The scape is removed because it eventually just turns brown and looks unattractive.
The fungus or mold in the mulch will not hurt your plants. It is part of the natural process of decay and helps the mulch break down naturally so it can feed the soil slowly over time. You can mulch over top of it if you wish or just ignore it. When conditions are no longer favorable (eg the mulch is drier or the particular material it is growing on is used up) it will disappear on its own.
Enjoy your daylilies!
Q&A Library Searching Tips