If i only ate 300 calories and drank a lot of water each day would i lose weight and burn fat from working out faster?

Yikes!: Only 300 calories a day would be very hard to manage long term- it's practically starvation! Likely to be very hard to stick with and I bet you'd be too fatigued to work out effectively. I would be less drastic. Try a healthy balanced diet with mild caloric restriction over the long term, this is much more likely to produce lasting success. Remember, slow and steady wins the race!