mums and "dust" bugs

My flower beds needed some winter color so I bought 4 or 5 chrysanthemums last fall. They are not my favorite, but beggars can't be choosers when it comes to January blooming flowers. And I do kind of like the daisy type ones. Anyway, apparently my garden is quite conducive to mums and they have been multiplying like crazy. I keep cutting them back, but they keep charging on. And some look like they are making buds. Do they bloom twice a year in warm climates? Being a cold climate native, I had always thought of them as annuals.

We have heard that the people who lived in this house before us were really serious chrysanthemum growers. Contest winning. Though their garden was razed and converted to a bare sand lot, maybe some of their magic remains.
In case anyone has been lying up at nights worrying about the lettuce and the red aphids. I am happy to report that though we lost the baby green lettuce, the red lettuce survived! I sprayed with diluted natural organic dish soap for a week and the aphids disappeared. They seem to have found greener pastures anyway, or maybe it is the end of red aphid season? I don't expect the lettuce to last long with this heat, but it would be nice if it hangs on until we have a few of our own cucumbers and tomatoes to round out the salad.
These are the sunflowers that reseeded themselves from last year. They are once again infested with a small bug that looks a bit like dust and makes dusty looking spots on the plants. What are they? Can they be driven away with diluted dishsoap? I've been spraying them for about a week. I haven't noticed any reduction, but they haven't multiplied either.
Here is a close up shot. Well, closer, anyway. They are awfully small.
They love the asters, and have almost done them in.