Herb Garden Expert? Help Needed...?

The bugs probably came with the plants when you bought them. Disposing of them was the right thing to do. They are probably the critters we call "white flies". Once they invade a plant there is no hope for revival. Here in east Texas cilantro,chives,onions,and dill start to die off in the late spring/early summer.The "tarragon" you referred to is more likely an herb called Mexican mint marigold. It doesn't do well in the summer either. But don't discard it or the chives ,when the weather cools down they'll start growing again (perennials). I suggest you get another parsley. They grow for 2 years - a real thing of beauty. It is my favorite herb to grow!