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Absolutely! This can easily be done under the right circumstances. This article will give you the information you need: https://www.gardeningknowhow.com/garden-how-to/projects/rooting-plant-cuttings.htm

Giving your pawpaw tree the environmental conditions it prefers will encourage healthy growth. See the following articles for pawpaw care and fertilization:

https://www.gardeningknowhow.com/edible/fruits/pawpaw/growing-pawpaw-trees.htm
https://pubs.ext.vt.edu/438/438-105/438-105.html
http://www.fruit.cornell.edu/mfruit/pawpaw.html

Yes, that can be fine. I would address what looks like a fungal infection starting, also. You can apply dolomitic lime and wettable sulfur to the soil and this will take care of the issue.

This article will help: https://www.gardeningknowhow.com/edible/fruits/pawpaw/growing-pawpaw-trees.htm

It is likely one of many fungal infections that can infect fruit trees. Many times this is incurable, but can be treated with some success using copper-fungicides during dormancy. The best way to keep it healthy from here is to provide the best environment that you can. This article will help: https://www.gardeningknowhow.com/edible/fruits/pawpaw/diseases-of-pawpaw-trees.htm

They should survive the temperatures, but burying them Pot-In-Pot style is, definitely, going to give the seedlings an advantage.

This article will help you to grow them in container: https://www.gardeningknowhow.com/edible/fruits/pawpaw/container-grown-pawpaw-trees.htm

Most will remain under 30 feet tall. Around 15 or 20 is common. Their spread can be up to 10 feet or so.

Here is an article for more information on the tree:

https://www.gardeningknowhow.com/edible/fruits/pawpaw/growing-pawpaw-trees.htm