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The best method of propagation from Astilbe is from divisions. You will want to take an area of the rooted plant and break it off, making sure that you have both roots, and shoots. You Will want to Dig an area, at least, big enough to double the root space. I would recommend digging as much as you possibly can, in order to provide the most space for roots to develop.

Here is an article for more information: https://www.gardeningknowhow.com/ornamental/flowers/astilbe/how-to-propagate-astilbe.htm

Astilbe can be optionally cut back after the foliage has died and turned brown. Or, you can wait until spring and then clear away the old foliage. Don't trim closer than 2 inches from the ground to avoid damaging next year's buds.

They should be cut to near soil level but not quite. About 2 inches above the ground is best.

I am not sure I fully understand the question, but this article should help with fertilization: https://www.gardeningknowhow.com/ornamental/flowers/astilbe/tips-on-feeding-astilbe.htm

It is still a bit early for leaves to be emerging in 6b, particularly in shady spots. A chilly March isn't helping! Plants respond to soil temperature, not ambient temp. However, the crown of astilbe is often very near the surface. Raking with a metal rake might even break off tender leaves. Many perennials show little above ground growth their first season; they are focused on root development. I expect you'll see growth in the next 2-3 weeks.

Yes, keeping them in container in a south facing window, or under horticultural lighting can help you give them a headstart before you plant them.