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As long as you meet their growing requirements, this should be fine. This article may help as well: https://www.gardeningknowhow.com/ornamental/flowers/bop/dividing-bird-of-paradise.htm

For the start, I would say that you should backfill the hole you plant it in with topsoil and compost. Make sure that the hole is twice as deep and twice as wide as the rootball. For the surrounding clay soil, I would recommend starting a regular schedule (yearly or twice yearly) of topdressing the area with organic material (compost, leaf humus, yard clippings, etc - even mulch will work). Over time, this organic material will work its way into the clay soil below and will help improve the soil quality of the entire bed. This will help when the BOP outgrows its initial hole.

You can cut it down about 1/2 way.

This article should be of help: https://www.gardeningknowhow.com/plant-problems/environmental/tips-for-saving-cold-damaged-plants.htm

If the plant is in bloom, you can send a picture so we can help identify it for you. Typically, the most popular type, Stelitzia, produces flowers that are reminiscent of flying birds - a telltale sign that you have this variety. This article will help with growing this type: https://www.gardeningknowhow.com/ornamental/flowers/bop/bird-of-paradise-an-exotic-flower-like-none-other.htm The other types, red, yellow and Mexican (which may also be red or yellow) look much different. Here is more information: https://www.gardeningknowhow.com/ornamental/flowers/bop/mexican-red-bird-of-paradise.htm

It is best to use a balance fertilizer with bird of paradise. Epsom salt really does not do much of anything for plants and aluminum phosphate would only provide part of what they need to grow well. Look for something that has a balanced NPK number (like 8-8-8,-10-10-10 or 20-20-20.