Fuel gauge not working?

I recently purchased a 2008 3.3L Sante Fe and after using up the gas that the dealer had put in, I noticed that I only got under 400 km on it. And when I filled it up from what I thought was empty (so the fuel guage said), I was only able to fill it up to 58L. Which I found weird because it has a 75L tank in it. I am keeping track of the amount of gas I am putting in and the distance I am able to travel, but I don't have enough data collected yet because I have not used up my first full tank of gas yet. My question is, if the Fuel Level sensor in the gas tank is reading wrong, could that effect the reading on the instrument cluster as the range I can go on the fuel left? Also, the distance per liter is also stuck at "13.5km/L" which I think is horrible for the vehicle. Regardless whether I am on the freeway or city streets, it is stuck at "13.5km/L:" I am going to try to run the car on the highway till I run out of gas and see if the fuel guage is reading correctly or falls short. I will update when I am able to get out of town. Thanks in advance.