Can a three phase motor run on a DC supply?
Yes, a three phase motor can run on a DC supply. You will need to provide an inverter, or a motor-generator set to do so. (In practical terms, the answer is no, because the costs will be high for any kind of significant power.)
No. You need a three phase supply to run a three phase motor. If you only have a one phase supply, you could use an inverter or a motor-generator set, but by the time you did that, it would have been more cost effective to simply get a one phase motor, or (in the bigger case) upgrade to a three phase supply.
A three phase motor requires a three phase power supply. You can not run a three phase motor on a single phase power supply unless you provide some kind of converter, such as a motor-generator set or an inverter. You might be able to get the motor to rotate on single phase, if you provide starting torque somehow, but you will not get rated power in that configuration.
What is the difference between a one phase and a three phase motor. And if a three phase motor is given a single phase supply will it run or not?
The difference between a single phase and a three phase motor is the amount of power conductors that feed the device. As to the other part of the question a three phase motor will not start or run on single phase. The phase angles on three phase are 120 degrees apart on a single phase system they are 180 degrees apart.
You have one hp three phase motor where as available power supply is only single phase how can you run this motor?
Shunt motors do operate on single phase AC. There are millions, if not billions of them worldwide running right now. Make certain your voltage supply is correct for your motor. Also, make certain you're providing the proper amperage. Make sure it's not a three phase motor. (three phase motors won't operate on single phase power.) If your supply voltage and amp supply is correct and the motor still doesn't run, you've got a bad motor.