The old diff will come out, the donor LSD will basically pop in in its place, I have no doubt that its not that simple, but because its an option on most of the cars, and the transmissions are all very similar it won't stress too many BMW mechanics.
I don't know about timeframes, but I'd imagine you're looking at 6 hours work given what it took for them to work on my diff and gearbox at the last service.
I'm not well read on LSDs - but they work by applying torque from one wheel to another, so as to avoid the wheel with less grip from slipping, main advantages are better traction under sprint starts (i.e at traffic lights ) and better cornering because of the extra traction
Still haven't chipped it - amn't sure if I'm going to spend more money on it - just got a quote of €1750 on an M3 Evo so I might just wait till December and get it. Had the car dynoed at 155BHP with just the exhaust and panel filter on it, but my O2 sensor was knackered so I lost between 5-10 BHP because of it according to Martin at Westward.
If I was to take 10BHP extra, and then get a Dastek Unichip - which is probably the best chip available for them - I'd still only be hitting about 179BHP, the car would be fast but not quite M3 fast... A lot of consideration to go into this one!!