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As long as the tree is not girdled, you should leave it to heal on its own. The bigger problem is the beaver. They are notoriously hard to keep off a piece of property once they've decided that the land is part of their territory. To protect this tree, you may want to try placing some chain link fence around the trunk 3-4 feet high or try a product called Ro-Pel.

There is no reason they cannot be transplanted. Because it is a magnolia, you may find that they are actually suckers. Even with these, as long as you make sure to dig up some roots when you take them out, they can be transplanted.

I am sorry to hear about your plants. Removing the ice would be good, but do so only with cold water. Warm or hot water will kill them. If they are still alive, make sure that ice does not build up on them again.

If the branch was completely severed, you cannot fix it. That branch will never grow as the "lead" branch again (which I am assuming it was) and grow upwards but others on the tree will take over for it and grow up. That being said, it will likely not grow as tall as it could have had the leab branch not broken.

You have a few options. First, you could try planting something that does well under trees, like ivy or pachysandra. Or, you could go with the rock garden idea or mulch the area, as long as the rocks or mulch were not too deep. You could also consider building a deck under your tree.

I would not advise adding additional soil. This would cause stress on the tree roots and would not correct the problem anyway as the tree would still continue to use up all the water and nutrients in the area.

This is going to sound very strange, but there is a possibility that it was snails. They are nocturnal and would have hidden in the deeper parts of the tree during the day, but they have been known to infest magnolias and chew up the young leaves and flower buds.