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Limited slip means it has a clutch pack inside the diff, to limit the slippage between the wheels. Only downside, is you must be sure to use a lube designed for a LS diff, or go buy LS additive from ford.
The bronco I am using as a donor for my 4wd conversion has 3.50 gears, but no LSD.
Is this axle going into your '81 F-100? Some early 80's used a car 5 x 4.5" bolt circle so make sure you don't run into that problem. The '86 has a 5 x 5.5" circle.
Not sure about pinion length. It might be that the pinion on one axle is longer than the other and you could run into driveline issues.
And make sure you carefully inspect the donor axle for excess pinion play, wheel bearing damage, axle in/out play, and wear and tear on all the gears inside the differential, unless you are just planning to do a rebuild anyway.
Brake hardware is interchangeable between the two axles so just use whatever parts look best. I would probably keep your wheel cylinders because if those parts sit for a long time they will leak.
And don't expect the limited slip to work. At all.
Honestly, if it were me I would just pull the 3rd member and have it set up the way you want it.