NMOS with gate source shorted and negative threshold voltage
First of all is it really possible to have a nmos with negative
  threshold voltage?


Yes, it's called a depletion mode MOSFET and, in your diagram, the MOSFET symbol is a depletion mode MOSFET: -



As wired in your schematic, M1 (being a depletion type MOSFET) is acting as a constant current source.

Picture from this document entitled "An introduction to Depletion-mode MOSFETs".

An example of a depletion mode MOSFET is the BSS126.