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I would wait to prune until you know what is actually dead or not. These are hardy down to zone 5, so you will want to leave this outdoors all year.

That is unfortunate about the predicament, especially now knowing that it didn't need to come inside in the first place.

It should recover, but the shape will not be the same. You will have to prune once you see what is still alive to attempt to reshape the damage into a more appealing form.

This article will help you to start shaping a bonsai: https://www.gardeningknowhow.com/houseplants/bonsai/first-bonsai.htm

Without a photo we can only make an educated guess; I suspect a "lichen". Lichen comes in different colors and growth habit; it grows on the surface and is not considered a disease, therefore there is no reason to remove it.

https://www.gardeningknowhow.com/ornamental/fungus-lichen/treatment-tree-lichen.htm

There is a slight chance it is a fungus disease, but I can't think of one that appears red on privet branches. There leaf spot diseases but fungus on the stems would be wood rot. If it's growing on exposed heartwood from a wound or pruning cut then it could be a wood decay fungus.

I'm not sure what you mean by "amoeba-like", unless you mean that it appears as formless and spreading on the surface, which could apply to lichen or fungi. Amoeba are microscopic organisms so if you can see it, it's not ameoba.

A picture is worth a thousand words you know. We don't always know the identification, but a photo sure helps. Don

There is not much that needs to be done now. You can cut the branches back a little bit after the weather warms back up some, but other than that it will recover on its own just fine.

Here is an article for more information on the shrub: https://www.gardeningknowhow.com/ornamental/shrubs/ligustrum/growing-ligustrum-shrubs.htm

These are adapted for a wide variety of climates. They do act differently in different climate zones. In many areas, they will lose their leaves. They can handle pruning, and often this will restore their vigor. Now would be the time to trim before the growth starts to get aggressive.

This is a type of Privet, or Ligustrum (Latin nomenclature) This article will give you more information on this shrub: https://www.gardeningknowhow.com/ornamental/shrubs/ligustrum/growing-ligustrum-shrubs.htm

Privet berries are poisonous for dogs as well as humans and the leaves can be even more toxic in large quantities. Toxicity is due to the presence of terpenoid glycosides.
You can call Poison Control to see if they have any toxicity info on plant contact.