They use the same kind of Automatic Transmission But there are two different manual transmissions. The grand Cherokee can use the AX-15 manual transmission which is bigger than the AX-5 but not the automatic transmission.
It does have a computer, no programming should be necessary.
On the starter.
Yes
Grand Cherokee parts would fit Laredo.
did you check the speedometer gear in the tranny?
Green.
If same engine and transmission models, yes.
Yes they should interchange without a problem.
What device is it attached to?
Transmission in Park, Transfer case in neutral.
Do you live in an area that you need your heater?
Dana 35 or Dana 44