1. Why does my car consumes more fuel if I have a burst exhaust pipe?

2.if I have droplets of water coming out of my exhaust pipe, what does
That say of my engine?

I think the catalyctic converter attached to the exhaust system is the reason for your fuel problem, not just the exhaust pipe. And the water from your exhaust pipe is condensation.

As for poorer mileage - the engine in your car is typically tuned to expect a certain amount of back pressure from the exhaust system. If the exhaust pipe is burst then exhaust gasses will exit from the engine cylinder prematurely, and some of the useful work that would otherwise be done by the expansion of the exhaust gas while still in the cylinder is lost.

Some people spend a lot of money for after-market "free-flow" exhausts that are touted as increasing horse power - you often see (and hear) these on small sporty cars around town. The irony is that is the exhaust isn't properly tuned to the engine characteristics you can end up with less torque and power out of the engine, not more.

The water in the exhaust is simply the product of hydrogen in the gasoline molecule combining with oxygen in the air to form water (actually steam) in the engine exhaust. If the exhaust system isn't up to operating temperature the steam may cool and condense out as water before it gets out the tail pipe. That's why you typically see water in the exhaust when you first start the car. After a few minutes the exhaust should be warm enough so that the steam doesn't condense out. People who use the cars primarily for very short trips may experience pre-mature corrosion of the exhaust components, because if the exhaust system never has a chance to get up to temperature water may collect inside the exhaust system and corrode components from the inside.