Hello, welcome to the forum.
The squiggly lines on the peppers are leaf miners. They are the larvae of a small fly. They cause mostly cosmetic damage. Just squish the lump at the end of the trail to kill the maggot. The leaf does not need to be removed it still can perform photosynthesis.
The pictures are not in clear focus, but the black dots do look like bacterial spot. It is a common disease of peppers. Preferably you want to get clean seeds as the disease can also be seed borne. Pick off those leaves to reduce the spread. If the spots are on every leaf, I usually get rid of the whole plant. It is hard to stop it once it gets all over and it just spreads to other plants. The cause is usually watering overhead and poor air circulation with plants being too close together and not enough of a breeze going through them to dry the leaves in a timely manner. Always water plants at the base and try not to get the leaves wet or splashed on.
The white things are also not in clear focus but they look like nymphs. The most common white nymph problem is white flies. But thrips and mites can also cause the stippling on the leaves especially around the veins and they cannot be easily seen without a hand lens or microscope.
Pests will always go after stressed plants. Since all these plants are together they not only transfer problems to each other, they are all equally being stressed. That is a cultural issue. For healthy peppers, they should be getting 6 hours of good light a day. They should be spaced 24 inches apart and have good air circulation so that the leaves can dry when they get wet.
Your soil looks composty and the pots look very solid. Pots need to have good drainage holes. More than one is better; holes on the sides of the pots are better too. If you have a composty mix, you need to be careful not to over water.
Potted plants need to be fed regularly, they are totally dependent on you for all of their requirements. Peppers are heavy feeders. 1/2 strength Miracle grow once a week should do it. Every 3rd week of the month only give the plants water, no miracle grow, to flush the salts from the pot. No saucers under the pots. Water thoroughly and drain the pots well, but don't water again until the soil is just barely damp. if the pots are taking more than 3 days to dry then your pots are either 1. too big for the plant, 2. the media is too composty and is holding too much water. 3. There is not enough air circulation to dry the plants out in a timely manner.
If the weather outside is over 70 degrees, they will do better if you harden the plants off and leave them outside. They must be introduced to more light gradually.
https://aggie-horticulture.tamu.edu/veg ... HT-038.pdf
https://vegetablemdonline.ppath.cornell.edu/factsheets/Pepper_BactSpot.htm
https://plantvillage.psu.edu/topics/pep ... ropagation
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