They are not connected, I routinely fatigue 2 DoL and rarely 3 in one day. Doing one has no direct impact on the others. And no, the fatigue system doesn't apply to total items, it is based on the total of successful gathers. At 150 total successes you begin to risk a successful action resulting in a damaged haul of items, and these become more common until by the time you've collected the 250th success, you can no longer gather anything successfully within the same class, until some time has passed.