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You can try to plant the seeds from grocery store peppers but there is no guarantee that they will germinate. Sometimes grocery store peppers are hybrids, which means the seeds are sterile. Other times, the peppers are irradiated for health reasons and this kills the seeds. It is worth a shot, but do not depend on them germinating.

You don't need to dry the seeds to grow them. You only need to dry them if you plan on storing them. You can plant them as soon as they come out of the pepper.

This article should help you with that: https://www.gardeningknowhow.com/edible/vegetables/pepper/pepper-fertilizer.htm

You should see your first sprouts in about 7-14 days, but some peppers can take as long as a month or more to come up. Pepper seeds are notorious for taking their time to germinate, or germinating at different times. Also, peppers won't even attempt to sprout if temperatures are below 60 degrees F. Here is an article that you may find helpful: https://www.gardeningknowhow.com/edible/vegetables/pepper/how-to-grow-red-peppers.htm

All peppers start out green. They should start to turn red a weeks or two after the peppers have reached full size.

White leaves are normally sun scald. Are the plants inside or outside? If they are outside, they were not properly hardened off. This article will help:
https://www.gardeningknowhow.com/garden-how-to/seeds/how-to-harden-off-your-seedlings.htm