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The black spots could be scale insects, or aphids, or even spots of sooty mold. A good treatment of neem oil should take care of whatever those are, as well as unwelcome diners.
https://www.gardeningknowhow.com/problems/pests/neem-oil-uses.htm

There are really no hard and fast rules for repotting. For most plants, if you can remove the pot from around the roots, and the roots are all matted inside and retaining the shape of the pot, that is called root bound, and repotting is probably a good idea, for most plants. Other clues can be there's so much plant that the whole thing keeps falling over, or it doesn't seem to stay hydrated no matter how much water you pour in. Other than these things, most gardeners recommend that plants be repotted annually, to renovate the roots and replenish the soil. Here's an article that talks more about repotting: https://www.gardeningknowhow.com/houseplants/hpgen/learn-more-about-repotting-houseplants.htm

Yes, you should wash herbs before drying. This article should help your project: https://www.gardeningknowhow.com/edible/herbs/hgen/how-to-dry-herbs-various-methods.htm

Unless you know for sure what the infectious agent is, I wouldn't eat the leaves. And of course, certainly don't eat if you've sprayed with a chemicals. This article on basil diseases may be useful to you: https://www.gardeningknowhow.com/edible/herbs/basil/basil-diseases.htm

You should do that with any basil plant. Cutting it back regularly will keep it from bolting (flowering). Once it bolts, it starts to become bitter.

There is still a possibility that the slugs are still getting to it. You may want to set out a small pan of beer inside the copper barrier to test whether it is slugs or not.

It could be rodents as well. What does the damage look like?