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You may not be able to keep this plant in a container for a long period of time.
Corkscrew Willow is fast growing and will outgrow a container quickly.
Keeping it pruned both above the pot and it's roots will help keep it contained.
Soil should be changed each spring to keep it healthy. A good quality commercial potting mix is fine.
Corkscrew Willow is a heavy feeder and you can help keep it compact by feeding it a 3-1-2 or 2-1-2 fertilizer ratio.

Make sure the container has plenty of drainage holes so you can keep an eye on the roots. When they start poking out, it's time to repot.

Watering is crucial, soil should be moist but never soggy. If roots dry out, the plant can die.

https://www.gardeningknowhow.com/ornamental/trees/willow/growing-a-curly-willow-tree.htm

We have corrected this article! Thank you!

Yes, you can propagate in that manner.

What you describe is most likely due to "early autumn leaf drop due to long dry summer" and not from the pruning of two branches. It should recover and leaf out normally in spring.

Soil fertility and water management are important for plant health and resistance to drought stress. Apply a complete fertilizer in the early spring, mulch the soil surface to help retain soil moisture, and water appropriately through the dry periods. Willows are water loving and grow on the banks of streams and ponds in their native habitat.

https://www.gardeningknowhow.com/ornamental/trees/willow/growing-a-curly-willow-tree.htm

Unfortunately, your photo did not come through. I am unable to see the damage.

Overwatering, or underwatering are possibilities. disease can be likely, as well, but it would be hard to say without photos.

In the meantime, this article will help you with the care of the tree:

https://www.gardeningknowhow.com/ornamental/trees/willow/growing-a-curly-willow-tree.htm

This could be due to a lack of nutrients in the soil. They will grow very slowly in this case.

Here are some articles to help you test your soil:

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

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/soil-ph-plants.htm

As far as toxicity goes- They aren't regarded as toxic. You would have to consume quite a bit for it to cause any negative effect at all.

All members of the genus Salix do contain Salicylic acid, nature's Aspirin. It is not concentrated enough to do any harm to you, though.

Here are some articles to help you to provide proper conditions for the tree:

https://www.gardeningknowhow.com/ornamental/trees/willow/growing-a-curly-willow-tree.htm

https://www.gardeningknowhow.com/ornamental/trees/willow/treat-peeling-willow-bark.htm