A timer can only produce pulses or interrupts of varying width but not of varying frequency as required by the stepper motors. I.e. one timer is sufficient to control multiple stepper motors, all derived pulses can occur only at a multiple of the timer interrupt rate.
Printing too much information about other timers etc. will not help, they only slow down the controller. Other parts of a program will use timers for other purposes, so dealing with only T3 will be sufficient.
In your case I suggest that you use a simulator or other means to test your program logic outside an Arduino. Then you have no real time restrictions, no interrupt priority problems, no processor overloading and whatever else will make testing of the program and class logic needlessly complicated.