Hello

I own a drone  with 1800kv a2212 bldc motors (the standard  golden ones) fitted with 10 inch 1050 props.
As I was flying them, one  motor refused to spin. The flight controller got the wrong idea, and caused the whole drone to flip.
No props were broken, nor was the drone. However, one of the motors' shaft broke  such that one piece was still inside and attached to the motor, and the other piece came off.
1) why did one of my motors refuse  to spin? All the motors did not start at the  same time. Is this a problem? also even when all  motors started at about 25% throttle, one of them refused to spin. Why?
2)What should I do now that  one of the motor shafts are broken? Should I buy a new motor of the same kind or buy new set of motors  of a different kind? or should I try and repair my broken motor? it still spins...

I have a TBS500 carbon fiber drone frame and as said before, 1050 props too. My flight controller is an omnibus f4 pro.
Please help me!

Try RE-calibrating the Flight controller , motors and all, and also check all the soldering connections. Yes if the shaft is broken , you need a new motor, its too much of a hassle to try to repair it yourself.

Also, always do testing with the props removed for safety purposes.