Answer to No.1

a) Vgs > VTn

The n-channel MOSFET is turned ON by applying a Gate-Source bias, Vgs, which is more positive than the Threshold voltage, VTn. That is, ON if Vgs > VTn.  This is because the sufficiently 'positive' Vgs (i.e., Vgs more positive than VTn) can attract enough negatively-charged carriers (electrons) to the channel region.

The channel region is the semiconductor area under the gate electrode.

You can verify that Vgs > VTn when NMOS is ON :