2002 is an F1 and no it will not fit into a C2 frame without modification. It's engine mounts are in different locations. So no 2002/2003 F1/F2 will not fit.
2000/2001 E1/E2 are similar engines and should fit, but their carbs are different than the 1998/1999 C1/C2, which may require some sort of airbox modification, depending on which set of carbs you put back on.
Your best bet is to either drop the motor and follow the threads in the 9R section on how to replace the C's transmission or find a working C1/C2 with a good transmission.