Engine swap
Hello , the swap its easy and you dont need different mount only that if you are going from a 4A-F to any engine code that end with " FE" your going from a carburated engine to a fuel injection engine , the "E" stands for ELECTRONIC . So my friend i would stick to a 4A-F engine...
The neutral -park switch is located on the tranny , where the shifter cable connects into the tranny its that way for all corollas even since the 80`s... The problem might also be in the shifter solenoid...You said, it only crancks when is running that tells me its in the interlock system not in...