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Since it is too cold outside for it, go ahead and bring it indoors unless you think it is too large to manage. In that case, leave as is till winter is over, but if another frost is predicted, cover the plant to protect it.
Once the danger of frost has passed, cut the damaged leaves off to the base. If the bulb did not sustain too much damage in the freeze, it should regrow from the bulb.
https://www.gardeningknowhow.com/houseplants/ponytail-palm/ponytail-palms-outside.htm

https://www.gardeningknowhow.com/houseplants/ponytail-palm/ponytail-palm-care.htm

I would not cut that out. The pups are usually on the side and have developed some roots in the soil. This will make a nice two-headed pony palm.

When you get some pups on the side, here is how to separate them:
https://www.gardeningknowhow.com/houseplants/ponytail-palm/propagating-ponytail-palm-pups.htm

No, there aren't many options. It is not recommended to cut it back because you would just leave a stump that is open to disease before it could regrow any leaves.

You can give it away or sell it and enjoy the shorter ones you have.

https://www.gardeningknowhow.com/houseplants/ponytail-palm/pruning-ponytail-palms.htm

As long as you introduce the tree to its new environment, slowly, then it should acclimate just fine. This article will help:

https://www.gardeningknowhow.com/houseplants/ponytail-palm/ponytail-palms-outside.htm

As long as they are happy, there is no reason to disturb the roots. If you feel that they are becoming rootbound, then this article will help you to transplant them:

https://www.gardeningknowhow.com/houseplants/ponytail-palm/propagating-ponytail-palm-pups.htm

I see previous signs of overwatering, but it seems that you are taking the necessary steps to correct this, already.

The potting mix and cactus mix will be perfect, together. You may need to play with the ratio before hand to get the texture just right. Once you feel that it is not too light, or not too heavy you can plant.

You should plant it, exactly, to the same level that it was, but if you would like to straighten it up a bit, then you can do so before covering the rest of the way with soil.

Here is an article that will help:

https://www.gardeningknowhow.com/houseplants/ponytail-palm/how-to-move-ponytail-palms.htm