I have quite a few daylily plants and some of the leaves on some plants are getting rust spots. How do I prevent this, and why is it happening?
This normally happens due to poor air circulation. You daylilies are probably growing pretty thickly and may need to be divided. This article will help you with getting rid of it:
https://www.gardeningknowhow.com/plant-problems/disease/learn-about-plant-rust-disease-and-rust-treatment.htm
How do I get rid of daylilies without using chemicals?
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.
My husband recently was spray painting our deck with exterior paint. He didn't bother to cover the plants around the deck and needless to say they got a spraying of paint. Will the paint kill the plants? Is there a way of removing it after it has dried?
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.
How do you care for the plants after the first bloom? The ones I have are supposed to continue blooming all summer, but I don't know how to prune them.
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.
Do I cut off seed pods so they will continue to bloom? I never know which plants to cut seed pods off or which I should leave alone.
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.
What kind of flowers is it alright to use cedar mulch for? I have heard that cedar mulch adds acid to the soil and should not be used with flowers, especially daylilies. Is this so?
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.
When should I divide my daylilies and how do I go about doing so?
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