1: How many gatherings do I have to do before this happens?
Difficult to perfect, but the higher average rank the items gathered is, the faster fatigue sets in. About 2-3 hours at grade 5, if you are quick to travel between nodes at lvl 50.

2: Is this one fatigue across all three disciplines, or does each one have their own fatigue?
Miner, Fisher, and Botanist have their own independant fatigue.

3: Does gathering with my off-hand tool affect it?
Fatigue is shared between mainhand and offhand