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Willow is one of the easiest shrubs to root using cuttings. Most articles recommend putting a cutting directly in damp soil. The planted end should have an angled cut. Rooting hormone doesn't seem to be necessary. To keep an eye on it and make sure the soil is moist, you can put your 6" cuttings in a container with regular potting mix. Branches that are still flexible tend to root faster than older, stiff wood. Late winter to early spring are good times to take willow cuttings. Mid summer, new growth can be trimmed for cuttings. They should root in approximately 3 weeks but it can be longer. A general article on taking cuttings follows. https://www.gardeningknowhow.com/ornamental/trees/tgen/how-to-root-cuttings-from-various-shrubs-bushes-and-trees.htm

Yellow leaves can indicate watering issues; too much or too little, disease or pests.
Do an examination of the bark, leaves and tree overall.

Stress & Chlorosis. A weeping willow's leaves may yellow and drop as a result of stress brought on by drought or the lack of regular watering. ... Chlorosis may also be a nutritional problem—a lack of trace elements, especially iron—due to poor drainage or compacted soil from foot traffic or construction.
I suspect your tree needs water but check it's overall health!
Balanced Fertilizer. A balanced fertilizer with an equal ratio of nitrogen, phosphorus and potassium, such as a 20-20-20 formula, is appropriate for a weeping willow. The nitrogen supports foliage growth on the tree's long, weeping branches, while the phosphorus supports the growth of roots, stems and flowers.

It is quite normal to receive a bare root tree. This is the most cost effective way to ship while in dormancy.

What you can do now is scratch the skin of the tree with your nail. If there is green under anywhere, or it looks like living tissue, then it will likely come out when it is ready. If there is no green anywhere at all, then your tree might be dead.

https://www.gardeningknowhow.com/ornamental/trees/tgen/tree-scratch-test.htm

Water sprouts can indicate stress or disease to the tree. They arise out of dormant buds and will often return when you remove them. Extension materials advise removing them as they rob the rest of the tree of essential nutrients and can make a tree look more like a shrub.

http://hyg.ipm.illinois.edu/article.php?id=993

It may be too far from a water source to stay healthy! These thirsty trees can suffer pretty badly when not in the right area.

Pruning and fertilizing can help it to return to a more healthy condition.

Here is an article that will help you to know what these trees require:

https://www.gardeningknowhow.com/ornamental/trees/willow/planting-weeping-willow-trees.htm