OBR / NCAA catch and carry

[bossman72]

Just need a few clarifications on catch and carry per OBR:

1) Fielder makes catch in LBT, then momentum takes him into dead ball territory where he goes down to one knee and one hand, stands up, and then throws back to the field.

Would you consider this a "fall" in OBR or "lost body control" in NCAA and award one base? What about 2 knees? Basically what I'm asking is (OBR) when is a fall considered a fall for the purposes of this rule?

2) Fielder makes catch while sitting/balancing on the top of the fence. His feet then flop over to the other side of the fence and lands easily on both feet and makes a throw back to the field.

Would you kill the ball when he lands on the other side of the fence and award one base? Does it matter if it's the outfield fence or a fence in foul territory?

Thanks guys!