I thought of that, too, but there is no need to be able to detect it from the other side of the earth. Timed depth charges and sensitive seismometers should be enough.
More ping pong balls also should work. The first few billion may get stuck along the ceiling of the cave, but if you drop enough, some will have to come out somewhere.
Only if the flow rate is high enough to defeat the buoyancy. Not guaranteed at all.
Also, there was no indication what the geography is within the hole. Organic material will eventually break down and waterlog enough to lose its buoyancy. Those ping pong balls and rumored car, though...
