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For the foundation, trees normally will not bother a foundation until they have nowhere else to go. If the roots of the tree are crowded by other foundations, then it might start to push on yours. You can think of it like a potted houseplant. As long as the roots have room to grow elsewhere, they will not push on the sides of the pot. But once it has no room for its roots, it has no choice but to push. I cannot speak to specifically if your tree has enough room or not for its roots. You would need a tree specialist there to determine that.

For the rats and snakes, yes this is possible as the roots will provide safe places for them to live. But, if you are able to make sure that other elements that would make the tree roots look like good homes are removed, the chances of rats and snakes moving in are much less. Making sure that there is not a ready food source (open trash cans, compost bins, etc) and attracting predators to the yard (like a pet mouser cat) will help keep them away.

I would recommend looking on eBay. Oddly enough, there is a great selection of hard to find, unusual plants for sale on eBay.

This article may help you with getting them to recover: https://www.gardeningknowhow.com/plant-problems/environmental/tips-for-saving-cold-damaged-plants.htm

The following article should be of some help to you:
https://www.gardeningknowhow.com/ornamental/trees/banyan/growing-a-banyan-tree.htm

This article provides info about banyan trees: https://www.gardeningknowhow.com/ornamental/trees/banyan/growing-a-banyan-tree.htm

This article will help:
http://www.floridata.com/ref/F/ficu_ben.cfm

You can try air layering as well.