Almost all the answers to these question have no true RAW interpretation and, as such, are solidly in the realm of DM adjudication.
The sphere will stop at the edge of a 15' pit (probably)
When you move the sphere, you can...jump it across pits up to 10 feet wide.
It is not clear why the ball will make it across a 10' casm without falling, but we know it cannot make it across a 15' one. As such, the flaming sphere probably would not even jump a gap larger than 10' if you tried since the magic just doesn't have that ability.
However, a if a DM were to rule that the sphere did not stop at the edge of the 15' pit (which does not seem that unreasonable), we know it would then fall as Jeremy Crawford has said:
Q: Is Flaming Sphere bound to the ground, given 3rd paragraph of the spell description?
A: Flaming sphere has no means of flight, yet the spell doesn't stop you from creating the sphere in the air. If you do, it falls.
Can you move it over water or some other less than solid or weak surface? - Not one greater than 10'
Refer to the quote above. I would rule that a 10' pit of water or fragile ice is similar enough that the ball of fire can jump over it. Anything greater than that would not work (and the sphere would fall or whatever surface appropriate effect).