All of those require fairly large pots, especially basil, dill, and mint. Basil should be in a six inch pot. Dill will grow up to six feet tall. Mint will take over your entire yard so it has to be confined. Mine is in a twelve inch pot outside. Cilantro can make it in a four inch pot but will do better in a six inch one. Same for parsley. My parsley re-seeded itself last year. It grew to eighteen inches high and the same across.
It sounds like you had too much plant for the available soil. You probably needed to water a little more often. The soil should not dry completely out, maybe halfway down and that's it. A plastic pot will need less frequent watering than terra cotta.
Fungus thrives where there is little air circulation. Based on your experience I would empty the pots, wash them with a weak solution of bleach to sterilze them and put in fresh potting soil.
I wouldn't be discouraged though. You will need to treat the larger plants as if they were bonsai. Keep them trimed both leaves and roots and they will be okay. Once in a while you will need to pull the plant out of the pot and see if it is root bound. If so you have two choices, trim the roots back with a sharp knife or repot in a larger pot. All of these need as much direct sun as you can give them.
I know that it sounds like a lot of work but once you've got them going it will be a lot easier.
Let me know if you have any further questions.