Any Idea what (free) programm I might use to give my image a particular length and height in pixels?
Inkscape or Gimp can rescale images.
Is the arduino capable of storing say 15000 variables?
No, why do you want to do this?
How does it draw darker and lighter spots?
The image pixels are made up by a number of pen passes, it is not one pixel per pass. The pen lifts and lowers several times to achieve a grey scale effect.