OP - You need to find out if your car has a bolted crownwheel diff. What year is yours?
And you need to ask the seller if he is selling just the internals or the whole thing in a casing (pumpkin).
If you have a bolted crownwheel type diff currently in your car then bingo, you can just transfer your own crownwheel onto the new diff and fit it straight in your existing casing, auto or manual transmission.
If you have a welded crownwheel (post 2007 ish) then it's a pain as you need to get your crown wheel machined off your diff so you can bolt it onto the new diff. (this costs about £300+ if you get it done)
E90 330i 6MT gone. E91 335i 6MT gone. AMG E63 Estate gone. M6GC current...