I have a FANUC SYSTEM 10 Type: A02B-0072-B501 That controls a Yam CK-1 Turning Center. How do i know if its a 10T or 10M? And if it is a model A or F...?

A02B-0072-B501 is a 10TA control. Basically, T stands for turning (lathe) and M for milling machine. A, B, C or D signifies different generation of a particular fanuc controller series. F is special though. It is for conversational controls.
For example, Fanuc makes series 0TA(late 80's)==>0TB(early 90's)==>0TC (mid 90's) for lathes (they came up with conversational control 0TF at the same time with 0TC). Same thing for milling machines 0MA==>0MB==>0MC & 0MF.