Okay, from the only evident off-roader on the board (other than Big Blue), here's the low-down.
More than likely, anything larger than a 31x10.5 will not fit correctly on your truck. As I say this, I'm curious, are they 31x10.5, or are they 265 series tires? I don't think I've ever seen a Ford that uses SAE tire sizes on their trucks (I don't get out a lot though

).
The reason they won't work properly (most of the time - this isn't true in all cases) is not because of the height of the tire and it hitting the fenderwells, it's because the added diameter, and width for most larger tires, will end up putting your tires into the frame, or the front bumper when you turn. If not for this, you could probably run 33x12.5 on your F150 easily as I could on my Toyota.
Personally, I wouldn't go any bigger than what came stock on the truck. Your mileage WILL drop (which is contrary to common sense, but trust me, it will), your brakeing distances will be longer and the brakes will fail sooner in hard stop situations, not to mention wear and tear on the tranny/clutch as the truck wasn't designed for use with larger tires.
To negate the mileage and tranny wear, you can put a higher gear in the differential to compensate for increased tire size. However, unless you're going for 35s or something, it's probably not worth it if all you want is bigger tires. You just have to drive a little more cautiously, keeping in mind the modifications you've made.
To answer your questions, however, no, it will not confuse the ABS, though like I said, your brake distances and responsiveness WILL drop, and it will not do anything bad to the xfer case (unless you go up a couple sizes, drop a higher gear in the differentials, and pin it to the floor when you're stuck - even then, the axle shaft will usually give long before the xfer case).
If you have any specific questions, PM me. I like truck and tires.