What's your question? Ask

You may want to consider solarizing the beds. This is very effective at killing viruses and bacteria that may be harboring in them and hurting your plants. This article will help: https://www.gardeningknowhow.com/garden-how-to/projects/how-to-solarize-garden-beds-to-eliminate-garden-pests-in-the-soil.htm

Either method would work, but tilling would get it integrated faster and you would be less likely to lose some of the added material to wind and rain.

Normally after the garden has died back, you can clean up any dead material. Discard any disease plant material and compost the rest. It can be helpful to put out a layer of leaves or straw to keep weeds down.

These articles may be helpful:
https://www.gardeningknowhow.com/garden-how-to/projects/fall-garden-clean-up.htm

https://www.gardeningknowhow.com/garden-how-to/info/cleaning-up-garden.htm

It is best to place a sheet or blanket in between the plant and the plastic. The plastic is actually a very good direct conductor of cold and also traps moisture inside, which increases how well the cold can get in. A sheet or blanket slows the transfer of cold and distributes the moisture more evenly. A plastic bag or sheet should only be used for keeping a cloth sheet or blanket dry.

As long as the plastic is not touching the plants this should be fine. YOu can also place water bottles of hot water under the bucket as well, to keep the air inside a little warmer overnight.

As long as it is not plastic, it should be fine. Here is more info on protecting your plants during a freeze: https://www.gardeningknowhow.com/plant-problems/environmental/protect-plants-in-freeze.htm