My rear differential broke unexpectedly, took it to a shop and found out that it was leaking because of a crack. Had to replace it

I also just had my transmission rebuild, could the two be possibly related? I never had any problems with the differential before.

Ever since I got the car, I had problems with the idle. It was pretty rough, lots of vibration. I changed the engine and transmission mounts, didnt do much...Anybody know what might be the problem?