Hi esp, i think i will try to answer some of your questions.
1) In this case you have to consider the fringing fields from your gate. If you use high-k dielectric i guess the electric field will not fringe too much and you can use smaller gate.
2) You should remember that the voltage drop you apply actually appears across the scatterer (i.e. the left source, the channel and the right drain region) all encapsulated in the middle box as a single structure. The electrode you use in ATK does not get voltage drop and is only there to provide self-energy for the left side of source and the right side of drain. In simple word if in your device structure if you ignore the left and right electrode box and consider the remaining structure, that is where the voltage drops.
for 3 I dont have much ideas to tell hehe