Why is fuel going down quicker than expected giving miles driven?

This is likely a result of lower fuel efficiency due to city driving and driving with a cool engine. Engines have an optimal operating temperature, which is normally around a couple of hundred degrees Fahrenheit. At this temperature, warmer engine fluids allow for less friction, fuel vaporizes and combusts more readily, and the engine is overall more efficient. In wintertime, a car's fuel efficiency can drop by 10-20% for these reasons. Even though you're in a warm climate, it's still well below the optimal engine temperature. Taking many short trips means that the engine is spending a proportionally larger time at below-optimal temperatures, and is overall operating less efficiently than if you drove the same mileage in one long trip. Shorter trips will also generally have more starts/stops than long-distance highway driving, which will also hurt your fuel economy - stopping and accelerating back up to speed costs more fuel than simply maintaining speed, which is why car manufacturers typically list both city and highway mpg.

This would explain why you're getting lower-than-expected mileage based on what you've had previously with longer trips. But if your fuel gauge is actually dropping significantly while you're not driving, I'd be a bit concerned. Parking on a hill can also mess with your fuel level gauge, so that could also explain differences in apparent fuel levels between shutting off and starting the car again.