how to check how many miles a car can still run while the fuel gauge is stuck on full?

Watch your odometer. Carefully calculate how many miles you get per gallon on the average, and use your mileage as a guide as to when to fill up. I wouldn't let it get below 1/4 tank.

The easiest way is to get a piece of paper. Write down the number of miles on the odometer. Drive it until it runs out of gas. Write the current odometer reading above the initial odometer reading. Subtract the initial odometer reading from the current odometer reading. If you passed second grade math, the resulting number will be the number of miles that you could drive from your starting point.

If you know how many miles per gallons your car gets and if you know how many gallons you have in your tank when it's full, fill up your tank and you will know how many miles you can go on a full tank before you run on empty.
For example:
You get 25 miles per gallon and your tank can hold 12 gallons. It means you can go 25 x 12 = 300 miles before you run out of gas.
Let's say, for example, your odometer shows that you already put 8600.0 miles on your car. You look at your odometer and you know you will run out of gas at 8900.0 (8600.0 + 300). But you don't want to push your luck, so around 8825.0, to be on the safe side, refill your tank.

Fill the tank up. Note the odometer reading. Drive it for 100-125 miles. Fill the tank again. Divide the number of miles driven by the number of gallons added. That will give you your approximate MPG. Determine what the capacity of the fuel tank is. For example, if it is 13 gallons, multiply 13 times your MPG. That will tell you how far you can drive on a full tank. So, you will have to fill the tank every time you buy gas, and note the odometer reading or set the trip meter to zero.