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Hello and thank you for your question. So sorry to hear about the damage. However it sounds like you have done the right things so far. Tieing it in place to give it support until the roots get re-established is a fine idea. I would recommend adding some good garden soils mix to the soils on that side of the tree that was uprooted. Mix some super phosphate in with that soil as it will help feed the roots and get them going. If you can get a product called Super Thrive where you are, then mix some of that with water and water your "baby" with that mix every 10 days for three or four cycles. The Super Thrive not only helps with the roots getting re-established but also with the shock factor. I hope all goes well.

Roseman Stan

If they are well established, they should be fine. Making sure you are caring for them as best you can is the best thing you can do to help prevent disease from getting in the pruning wounds while they heal. If you have not already read it, here is an article on their general care: https://www.gardeningknowhow.com/ornamental/trees/eucalyptus/tips-growing-eucalyptus.htm

This is not normal. It may be that the plant has some air pockets around the rootball that were not filled in correctly when the plant was put in the ground. Step firmly around the base of the tree to try to collapse these air pockets. Also, water the plant quite a bit as this can also help to fill air pockets in.

If you get freezing temperatures, the eucalyptus trees will not survive. But, this article has other trees listed that may suit your needs:
https://www.gardeningknowhow.com/ornamental/trees/tgen/wet-soil-trees.htm

Eucalyptus roots tend to be shallow compared to other trees, going down about 6-10 feet normally. Therefore, it shouldn't pose much of a threat to your foundation; however, since this type of tree can be quite water hungry, its roots will tend to wander in search of water when not enough moisture is provided (most foundation planting areas are typically drier), which can ultimately lead to issues later unless you can maintain adequate moisture.

Lost scent is often linked to a nutrient deficiency. Have the soil tested and fertilize the plant.