Yes, you can use the RA40 diff in your KE70. I had one in my AE86, it bolted up fine although the trailing arm mounts aren't in the exact same position as the standard diff. I think with the standard trailing arms the diff was pointing slightly up compared to the standard diff but if you have adjustable arms then no problem.

You will be able to fit any T Series centre (AE86, T18, etc) into the RA40 diff but just be aware of the zenki and kouki LSDs, RA40 T series uses the smaller Zenki axles.
I had a TRD 2 way in my RA40 T series, the axles were slightly too long for the 2 way so i just grinded a couple mm off the end of the axle. Im not sure if you could just use ae86 axles as the whole ra40 diff is overall longer (~40mm?)