The water is slowly draining into an airtight cavity underground and replacing air in the cavity, which is bubbling up through the same hole. The cavity is probably why you have a puddle there to begin with, the ground is depressed into the cavity. It could end up forming a small sinkhole. Excavation recommended.

Might be an old, long abandoned pipe that finally cracked? Air that has been trapped underground gets this stale, sewery smell. They lighter might have just been blown out by the water spray ejected from the popping bubble.

Air.