Is there a problem with planting a vine crop (squash) under cherry tree?
Yes, they should be compatible and should do well together. The squash won't get as much light as if it were growing in the open, but it should do fine anyway. The only issue is that you should clean up fallen or rotten fruit from the cherry tree or the squash plants promptly to avoid an insect problem
Hubbard plants have yellow leaves bottom outside perimeter
This article will help you.
https://www.gardeningknowhow.com/edible/vegetables/squash/why-squash-leaves-turn-yellow.htm
I harvested a Hubbard squash and a blue pumpkin, can I wash it as I still want the stem to dry completely
Leaving that dirt on it will help prevent infections and protect the fruit. I would not advise this until the stem is, completely, dry.
This article will help: https://www.gardeningknowhow.com/edible/vegetables/squash/hubbard-squash-care.htm
Blue Hubbard is overtaking area and soon will be going over stone wall onto sidewalk.
Constant pruning can help with invasive species. This article will offer more suggestions on controlling aggressive specimens in your garden:
https://www.gardeningknowhow.com/plant-problems/weeds/aggressive-garden-plants.htm