As this is only your second time working with electronics, I'll try to keep my terminology simple.
It's hard to see exactly how you have wired up the sensor and LED, but I can take a guess. (If I'm wrong, then everything below probably makes no sense).
The sensor is connected between + power and the Arduino input, while the LED is connected between - power and the Arduino input.
When you press the sensor, electrical current can flow from the + side of the power the Arduino sensor pin, charging it up and giving it a high voltage. Current also flows through the LED, causing it to light up.
Now, what happens When you release the sensor? The electrical charge inside the Arduino sensor pin which was giving it a high voltage, will now flow as current through the LED to - power, bringing the voltage down, so that the Arduino sees you've let go.
But what happens if you don't have an LED in there? The electrical charge in the Arduino sensor pin has nowhere to go, and so it just stays there, and the voltage doesn't change.
The reason the Arduino's sensor pin behaves like this is because it behaves like a tiny capacitor. It can store a small amount of electrical charge, and thus 'remember' the voltage that was placed on them by the sensor.
So, how can you fix it? You'll need to have somewhere for this charge to flow. If not an LED, then a resistor should do. Any value between 1k and 1000k will probably work fine.
See this page http://beagleboard.org/Support/FAQ
You need to have a 3.3 V serial adapter. A voltage divider is ill advised, because you need to maintain low impedance and you don't want to draw that much current on either side. If you insist on using the 5 V, then an active level shifter is recommended.
It is not surprising that it worked on the Atmega. Most microcontrollers will have pins that will tolerate 5 V.
Best Answer
Different positive and negative readings on a dual-slope ADC can be caused by the maker using a crummy integrating capacitor with a large amount of dielectric absorption. It's also possible the battery is dying and the integrator is saturating on one side but not the other.
Your other issue sounds like a grounding problem.