For the point 2.

I see that no one has suggested to use document.elementFromPoint(x,y), to me it is the fastest way to test if an element is nested or hidden by another. You can pass the offsets of the targetted element to the function.

Here's PPK test page on elementFromPoint.

From MDN's documentation:

The elementFromPoint() method—available on both the Document and ShadowRoot objects—returns the topmost Element at the specified coordinates (relative to the viewport).