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Banyan trees can be pruned easily at the start of spring and throughout summer. Prune back as much growth as you like (up to a third of its growth or more), as they're quite hardy.

It can actually take months for a banyan seed to germinate. It may be easier to propagate this tree through cuttings instead.

I think it would be very difficult to grow grass under the tree. Not only do you have poor light under it, but trees normally use up all the water in the area as well. So you need a shade loving, drought tolerant ground cover. Ivy is the standard for this but creeping juniper would work too.

Banyan tree don't general have dripping sap problems, so I suspect that the issue is actually that you have a pest problem on the tree, such as scale or aphids. These pests produce honeydew, which can drip off the tree and make a sticky mess. Treat the tree with a pesticide. The honeydew should wash off the car, but it may need much water. It is a little like melted sugar candy.

Yes, it should grow. Here is an article that you may find helpful: https://www.gardeningknowhow.com/ornamental/trees/banyan/growing-a-banyan-tree.htm

I think you might be overwatering it, though i might be wrong. sorry for such a vague answer but hey i'm just a kid!