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the ponytail palm is a slow grower, this will explain how to propagate the babies, which are called pups:
https://www.gardeningknowhow.com/ornamental/trees/palms-trees/propagate-palm-pups.htm

OK, so I don't really know how to answer this - most people don't prune ponytail palms, and I've never tried to root a piece. But if I had a piece of trunk, or one of the side shoots that sometimes come up, I would put it in wet perlite with a plastic bag over it as a mini-greenhouse, and be very patient. But I do know that this is the only part that could root; the leaves will not. Let me know how your experiment works out.

That is ok. They are just pups and are how the plant propagates itself. This article will help you with removing them and starting them, if you would like. You can always share them with friends. :)

http://www.walterreeves.com/gardening-q-and-a/ponytail-palm-propagating/

When my now 38 year old ponytail bloomed, it was about 13 feet tall and single stemmed. Living in zone 6, the plant was too large to bring back inside, so I cut it back to let it send out multiple stems. Four years later, it is prettier than ever with 8 stems and lots of foliage. Hope this helps.

My oldest ponytail, 45-50 years old, has been a member of the family 39 years. It bloomed once, about 7 years ago. Since the bloom spike was 15 feet in the air, and each bloom was so tiny, we didn't see any differences. No seed were produced. Sorry for not having a more definate answer to your question.

Assuming you want to relocate the plant, here is what I'd do. Dig 18-20 inches out from the caudex, (bulb/bottom) to a depth of 18-20 inches below the caudex. With a plant this large, you will have to have equipment to lift and move. My largest ponytail is about half the size of yours, and we lay it down and roll it, but it is in a container. Since most succulents don't have a huge root system, they usually aren't traumatized as dramatically when moved as leafy/tropical plants. Water the plant in, then keep new location barely moist until re-established. Kept too wet, the plant might not live...remember that caudex is like a sponge full of water.