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 :