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Earthworms! If you can't dig the ground, earthworms can loosen it and add some texture to the soil.

Be sure to mulch for them, so that they have a place to hide from the sun.

Here are some articles that will help:

https://www.gardeningknowhow.com/composting/vermicomposting/benefits-of-garden-worms.htm

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/how-to-attract-earthworms.htm

https://www.gardeningknowhow.com/special/organic/how-to-easily-improve-your-clay-soil.htm

This article should help:

https://www.gardeningknowhow.com/ornamental/groundcover/english-ivy/kill-english-ivy.htm

I would look online at other sellers and see if their cuttings come rooted. I think customers would expect rooted products.

You don't need to put anything on the bark. The vine above the trim should die. However, it may regrow from the roots if you did not remove all the roots. (I would use a non-selective herbicide if you see them returning.) Those vines are very thick, I would be worried about damaging the bark by pulling off the vine. The vine should die and slough off on its own, or you can pull it off then.

https://www.gardeningknowhow.com/ornamental/groundcover/english-ivy/english-ivy-tree-damage.htm

Sand works best, but you can try a combination of potting soil and perlite and using rooting hormone. The other thing you can try is rooting your cuttings in water. Here's an article that may be helpful:
https://www.gardeningknowhow.com/garden-how-to/projects/rooting-plant-cuttings.htm

Yes, it can take full sun to part shade, but you will need to slowly aclimate it to its new surroundings.

https://www.gardeningknowhow.com/houseplants/hpgen/move-houseplant-outside.htm