How can I measure the point of contact between two wires?
you could try 4 terminal sensing.

I have not used it myself, but the basic idea is to try to normalise for some of the external factors you mention.

As for the Arduino, the analog to digital converters have 10 bits of precision. This means you will get 1023 distinct values as the input voltage varies betwee 0 and Vmax (+5 or +3.3 depending upon the actual device). So that is fairly precise, usually you just use the value from the analog read - but you can convert to a value between 0 and 1 by dividing:

    int analogInt = analogRead(&lt;your port here- e.g. A0&gt;);
    double analogFloat = analogInt / 1023.0


Which begs the question, did you try using a 2 wire system? Assuming just 1000 data points, and a finger being, say, 5cm in length; that's roughly 1 point per .05 mm. I know it won't work out exactly like that, but that is my point - it is likely to be a rough estimate anyway due to the size of a finger at the touch point.