Are the fuel gauge meter suppose to be like this? (Honda Accord 2002 SE)?

I have an Honda accord 2002 SE. The question I have is I've seen other Honda's and vehicles have it so when the car is turned off the fuel gauge meter rests on empty (E). But with my car I've noticed that when I turn off my car the fuel gauge rests at the same spot and doesn't come down to empty. Nothing else is wrong it shows the correct positions but I wanted to know if I should be concerned that it doesn't come down and rest on empty. Also another concern I have is when the tank is low the fuel light shows up for a minute or so and then disappears for a while and comes back on. Would this be normal or do I need that checked?

I think mine goes down when I turn the car off. If it otherwise works fine, then I wouldn't worry about it. As for the gas light, that's normal. Since it's based on a sensor in the tank, it may indicate low, then go back to normal because the gas is moving around in the tank. Mine triggers more easily when I drive uphill. Mine also has over three gallons in reserve when the light comes on, so I always reset my trip odometer and watch the miles until I can make it to a gas station. Usually it goes around 100 miles or so before it will run out depending on the driving conditions.

All normal. The data sent to your gauge is from a float, not a sensor. It is behaving as it should. And because of the float the low fuel light fluctuates as you drive.