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Yes, large trees are recommended to be at least 25 feet from structures, though I would even suggest further.

Dappled Willow is one of my favorites.
You may want to do some light pruning while it's still spring. This plant also likes lots of moisture at its roots, so deep watering is in order. See if a bit of trimming might bring it back to health. Here's an article that should help:

https://www.gardeningknowhow.com/ornamental/trees/willow/dappled-japanese-willow.htm

Check the leaves for insects that may be sucking the sap out of it. Also, since it's in a pot, make sure it is draining well. They don't like wet feet.
https://www.gardeningknowhow.com/ornamental/trees/willow/dappled-japanese-willow.htm

Each time that you pot up, you will need to choose a container that is 1 or 2 inches larger on each side, until the tree stops filling out the container with roots. Make sure that the tree is relatively rootbound before transplanting each time.

Here is an article that will help with the care of the tree:

https://www.gardeningknowhow.com/ornamental/shrubs/pussy-willow/weeping-pussy-willow-care.htm

You may be referring to the dappled willow cultivar named 'Hakuro-nishiki.' It is hardy in zones 4-9 so that covers you. Its new growth is sprinkled with pink and is easy to find in nurseries in springtime.

You are correct in that weeping cherries prefer average water needs.

Here is some information that may be helpful.

https://www.uaex.edu/yard-garden/resource-library/plant-week/willow-dappled.aspx

https://www.gardeningknowhow.com/ornamental/trees/weeping-cherry/weeping-cherry-growing-tips.htm

If the container has no drainage holes or it remains wet for long periods of time in a confined container, it likely has contracted a fungal infection. Be sure and let the soil dry out between waterings. Papery leaves also can be attributed to lack of moisture, too much fertilization, or sensitivity to chlorine and minerals in the water if it isn't getting rainwater.