To visibly notice a lower reading on your fuel gauge, you'd have to be losing a considerable amount of fuel via a leak somewhere, don't you think? I have to think there would be a very strong odor of unburnt fuel at all times due to the fact that the fuel system is pressurized. Can you smell fuel when the car is off? If not, I'd manually check your mpg over the next couple of tankfulls to see if mileage is consistent. I'd bet on a faulty fuel level sensor before a fuel leak if there is no odor. If there is some odor, I'd check the FPR to see if it needs replacement.
At start-up, the stumbling could be many things. Is there any visible smoke at your exhaust tips under start-up. Excessive white smoke during the 'stumbling' would be bad, as you might be burning some accumulated coolant due to a leaking head gasket. Excess fuel in the cylinder(s) should cause a uniquely noticeable smell in the exhaust, but the presence of coolant isn't a normal smell either. If you don't have these conditions, I'd suspect your problem is electronic. Pull codes and see if the car is trying to tell you what's wrong before you do anything else. Good luck!