I wanted to use an old motor available and see if i can run it, when i was checking the back emf and the hall signals by hand rotation i observed the below waveforms, after looking at the waveforms i feel the motor is damaged is it correct? The motor details are as below, the hall waveforms are abnormal with short pulses in between.

 

Do you get the 3ph sine wave from the power windings themselves?

 

When i run the motor with hand and connected the phase to phase with differential probe I get the above waveform it is kind of trapezoidal waveform I have shown in the diagram.

 

Looks normal (a several second, constant motor speed spinning trace would be nice) when the three hall sensors are triggering. Turning the motor by hand is noisy and slow, so are the trigger edges. The trapezoidal waveform is perfectly normal for a BLDC motor designed for 6 step commutation.
https://www.ti.com/lit/ml/slyp711/slyp711.pdf

 

If you are rotating the motor by hand there will be jitter in the movement, which could result in the spurious spikes in the Hall signals.

 

This is typically the waveforms obaserved when a motor is back-fed.
Used to align Commutation sensors.
BTW Hall sensors are a little passé now, usually optical is used for accuracy.