Liquid fertilizer is good at this point help plant recover afternoon shade help sun loving plant 8-4-4 be garden center other jesting fertilizers good long term in link. When buy potted plant short time they be hungry.

Here is a link that might be useful: Herb Fertilizer 8-4-4

Did you ever fidure out anything? Mine looks the same

Basil gets that blackspot a lot I find from watering and having the soil splash up, its pretty common. I would suggest mulching around the base when they come up next year with pinestraw. Skip the commercial mix and go with something like black cow manure and mushroom compost. Or mix in peat and cow manure along with a commercial mix and it will cut down on this as well. I have found that basil needs to stay wet to grow a lot, but also needs to be dry. It is very similar to mint and salvia in growing requirements. It is also the time of year when basil goes to seed in the deep south as mine is doing so I start into watering the base once a week just for seed production as the rain just slowed down. Try to not splash water, I treat basil like roses.