Thevenin equivalent of nmos
Since we are trying to find the Thevenin impedance, we would have to compute the impedance looking from the load , in this case I think that it would be from the source of M1 (considering your final equivalent circuit) . So looking from Source of M1 if you draw the small signal model and derive you would obtain an impedance approximately 1/gm1 [ 1 ] . 

If you draw the small signal model for the circuit in the left side, you would get something like this,

 

And further using KCL and KVL you will realize that v/i = (Rd + rds) / (1+ gm1*rds1) = 1/gm1 (approximatelly considering Rd = 0). So therfore this explains the 1/gm1 part.


  Here if we zero out vin1 we will be in a situation where mos will be
  off, right?


Remember that the MOSFET is not necessarily off if Vin =0 because to turn on the MOSFET we require a Vgs=Vg-Vs>= Vt and if Vg=0 then Vs can be >= -Vt,  thereby turning the MOSFET on. 

And for the thevenin voltage I am also not very sure  but I think it could be something like this, since to find the Thevenin voltage we will have to remove the load which in this case would be the right hand part of the circuit we would be having only the left hand part with the source of M1 hanging (unconnected or high impedance). Since no current flows through the left hand side Vgs cannot be more than Vt because if it is so, then some current should flow ! So to satisfy this criteria if you assume Vs = Vin then Vgs = 0 therby satisfying the no current condition.

[ 1 ] http://web.iitd.ac.in/~shouri/eel782/lectures.php, refer to the input resistance section (the image is also from the same link).