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If part of the tree is still alive, it can survive but, unfortunately, it will be deformed. Once the main trunk is killed at the top, several side branches will take over to become trunks. Even if only one branch steps forward, the tree will be oddly shaped. Pruning itself will not harm the trees, but they will not regain their former shape.

If it's broken along the branch, you could use bamboo kebob skewers or popsicle sticks as splints, and string or yarn to wrap the branch so that the broken pieces are held together; in time, new tissue should grow. If the branch is broken at the trunk, use string or yarn tied from the broken branch to the trunk or the branch above, so that the broken part is held up to where it's supposed to be, then wrap branch and trunk with tape, any kind, doesn't matter. Once again, new tissue should grow.

This article has propagation tips: http://mrec.ifas.ufl.edu/foliage/folnotes/norfolk.htm

No, you do not need to prune sago palms. They actually do better without being pruned. It likely is shock. A little fertilizer that is high in phosphorous and consistent watering will help, but other than that, it just needs time. Many plants will recover just fine from shock so I would not lose hope for it.

Cutting one or two exposed tree roots is not recommended as a control method, except as a last resort. There are some other things you might try first, as in this article: https://www.gardeningknowhow.com/ornamental/trees/tgen/exposed-tree-roots.htm

Seed pods, yes. Your tree is a female, and there would be a male close enough for pollination, so every few years you can expect seeds. A shop vac is a handy tool for picking up the sharp little seed pods.