Value of an sensitive Analogsensor changes heavy with other power sup. than USB

I plug in all 3 pins (Vcc,GND and Signal) in the Arduino, then I measure with my multimeter the resistance between the 2 Pins of the sensor and get 300 OHM its not impossible, its the truth.

You cannot measure resistance with the power on.

The resistance of the sensor must be measured with a multimeter across the two outside pins of the sensor with them disconnected from the circuit.
Also, you have not posted any voltage measurements at the arduino analog input pin taken while running your test code.
As I said previously , until you can post a photo of a multimeter on VOLTAGE (DC) SCALE showing a measurement of 2.5 Vdc
at the arduino analog input pin , I will not believe that your circuit is working . I have given you all the calculations . I have explained how to test and still you have not measured the voltage, your measurements of the sensor are not taken correctly because you had the sensor leads connected to the circuit:

I plug in all 3 pins (Vcc,GND and Signal) in the Arduino

you were supposed to put the sensor in the Prony brake and measure the resistance across the wiper and GND leads while applying 1 lb of force on it and then with no force. The sensor doesn't have any circuitry, it is just a poteniometer so you don't
need the Vcc lead to measure the output. The only thing you care about is the Vcc lead to GND lead resistance because the datasheet shows the wiper (center lead) is "NC" (Not Connected)

The resistance for NO LOAD is about 1 MOHM (and not 10 MOHM as I thought and the tutorial for the 25 lb version mentioned so the value of the resistor is wrong?!
should be about 500 KOHM ???
The resistance for MAX LOAD (more then 1 lb is about 60 KOHM.

Where did this information come from ?
Did you measure these values yourself using the Prony Brake ?
Have you ever measured the VOLTAGE on the arduino analog pin while using the Prony Brake at 1 lb ?
Or with No force ?