Not familiar with EK's ops at Cairo, I do believe T2 is the new terminal, not sure if its open yet. I've only flown in and out of T3 with MS.

I have heard however (not sure where so don't treat this as confirmed) that there is a shuttle bus between terminals (possibly landside but you can skip immigration to take it if you have an onward ticket to show). I've had 2 long transits in CAI where I've been in the MS complimentary transit hotel which is landside but with no visa or stamp, they simply confiscate your passport, so immigration does seem open to some shady skipping back and forth kind of deal. When going through passport control on departure you just tell the guy who checks stamps that you're a transit pax and he doesn't check further, despite you not showing any evidence of such, so it does seem like a lot of holes in their immigration net.