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This flower shape is present with, both, Asters and Thistles. If the leaves have spines then I would be inclined to say Thistle. If the leaves are spineless, then I would be inclined to say that it is an Aster species.

Here are some articles that will help:

https://www.gardeningknowhow.com/plant-problems/weeds/canada-thistle-control.htm

https://www.gardeningknowhow.com/ornamental/flowers/asters/growing-asters.htm

Absolutely! This article will help with how and when to do this:

https://www.gardeningknowhow.com/ornamental/flowers/asters/spitting-aster-plants.htm

Yes. As part of your spring cleanup, you can cut back all summer and fall blooming perennials that weren't cleaned up in the fall. I wait till spring to cleanup to give plants an extra shield against cold weather and in case any butterfly caterpillars are overwintering.

Just cut it to the ground, avoiding any new foliage that may be coming up.

I couldn't find any reference to an aster that closes at night, but Michaelmas daisy is a popular one in Australia.

https://www.abc.net.au/gardening/plant-finder/aster/9441268

You can wait to see if they all have it, because it's possible the leaf hopper skipped a few plants while feeding. Only the plant material is infected and can only be transmitted by a leaf hopper injecting his saliva into the plant.

https://www.gardeningknowhow.com/plant-problems/disease/aster-yellows-disease.htm

No, asters are deciduous. I have a cousin in nearby Illinois that has an evergreen Golden Mops (a.k.a. Chamaecyparis pisifera, or Sawara cypress). You can also use ground juniper, also called Common Juniper, Old Field Juniper, Prostrate Juniper, Juniperus communis var. depressa.