Trying a crude water level sensor first of all, Im from Cuba, that means I may have some problems to find parts... 

I have a little system to measure the water level in my house water tank. The system is pretty rough: a proximity sensor HC-SR04 well fixed in the top of the tank, some long wires to an ArduinoNano, and a LCD screen where I display information as: water level in liters and in %.

The problem is the proximity sensor HC-SR04 seems to be broken now, not work at all and I was thinking in replace it by raw cables

Something like in the image below, but maybe with more steps:


So... My questions are:

-Is this posible? I just test it with a glass of water and two short wires and it work, but sometimes it throw me some falses-positives... It may be my code: just light on a led if digitalpin X is high when I put two wires in the water (1 wire to arduino 5V pin and the other to the digitalpin I wanna check if is high), and it do it, but when I pull out the wires the led stay on for more than a few seconds. 

-If it is posible, how long can be the wire? Is 10m ok? 

Thanks
As others have said, you need to make sure you have pull-up or pull-down resistors on all digital inputs so their value doesn't "float" (fluctuate between high and low.)

Given that water tanks and wells tend to be strongly earth grounded, I would suggest some changes:

Change the common wire to a ground, not +5V

Change all of your other pins to analog inputs. Connect them to high ohm pull-up resistors (say 10kΩ). They will read a full 5V when their ends are not in water. When the water rises and the ends dip into the water, their voltages will drop. Use analog readings to detect those voltage drops.

You could also use something like graphite a pair of graphite rods in the water, and a voltage divider circuit. As the water level rises, the current would travel through less graphite, and the resistance would drop. I don't know if that would give you enough top-to-bottom measuring distance.