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Dig out as many of them as you can then pour boiling water all over the area to kill any roots that remain. Be aware that boiling water is a natural "roundup" plant killer. It will kill any plant material it comes in contact with, so make sure that you protect any desirable plants.

Depending on the type of paint, it should definitely be removed. You could try wiping it down with rubbing alcohol to remove the paint or a product called Graffiti Go, which is probably less harsh on the plant. Once removed, you'll need to wet down the plants thoroughly to wash away any chemicals that may be left. Alternatively, you may just want to trim off the painted foliage.

No pruning necessary. Just cut off all spent scapes (bloom and stem). Some daylilies are "reblooming" and will give you another set of blooms later in the season. Some are "extended" which provide a long season of bloom. Some bloom once a season and that is it. I don't know of any that bloom all summer, however. They need a rest period.

Removing the spent blossom stalk will just make it look better. In general, most spent flowers from plants is a good idea. Certain varieties of plants will bloom longer or perhaps rebloom and if not done, the plant thinks its job is done and shuts down. That is particularly true of annuals.

The cedar mulch should be fine. However, you should have a soil analysis done beforehand, so you have a general idea of what kind of soil you have. Cedar mulch does acidify the soil some, but slightly acidic soil won't harm most plants. If you're worried about the acidifying effect, add some limestone to the mix, or sprinkle some on top of the mulch.

Dividing perennial plants can be done in fall or spring, depending on the plant, where you're located, or personal preference. This article can help: https://www.gardeningknowhow.com/garden-how-to/propagation/propgen/dividing-plants.htm