I have a 0.5 kW single-phase AC motor. What happens if the supply is 220 V but can't supply the full current needed? Will the motor torque be lower? Or will it be slower?
Will it be any different if this motor is a water pump motor?
Torque is proportional to current. If you can't supply the full current, then the torque will be lower than it would be otherwise.
The highest current draw is at startup when the motor is not turning. This means the motor will produce lower than intended torque when it tries to get going. If this torque isn't enough to get the motor moving, then it will just sit there getting hot, and the current requirement won't decrease.
Another point is that you supply can't be 220 V when it's unable to supply the current the load is trying to draw. Something has to give. This could be the supply putting out lower than 220 V, or it could be popping a fuse or breaker, or possibly melting or otherwise destroying something.