Parasitic capacitance in real resistors 
Typically, I'd assume (A) is only a justifiable answer when the two metal end caps have essentially infinite area, or when the spacing between end caps is far smaller than their respective areas, in which case we can ignore fringe effects, discern the electric field as some form of magnitude like $\sigma / \epsilon$, and declare it a capacitor. 
However, here this seems to be a capacitor despite not knowing anything about the comparison between the spacing between the end caps and their areas, so I don't see why we can ignore fringe effects and all that. Why can this be assumed here without notion of end cap dimensions and spacing?
 A: We are not ASSUMING that there are no fringe effects.  We are DEDUCING that there must not be any such effects within the resistor.
There are probably many ways to arrive at this conclusion, but I find it illuminating to suppose that there are in fact fringe effects within the resistor.  Then at some point just inside the top edge of the resistor in your diagram, the electric field would be at an angle to the edge of the resistor.  Thus there would be current flowing at such an angle to the edge, which would change the distribution of charge on the edge of the conductor (since the charge can’t continue flowing outside the resistor).  Thus our supposed electric field is not an equilibrium state, and any equilibrium state must have a uniform horizontal electric field within the resistor.
A: 
Typically, I'd assume (A) is only a justifiable answer when the two metal end caps have essentially infinite area, or when the spacing between end caps is far smaller than their respective areas,

I think you're meant to assume the spacing is very large relative to the lateral dimensions. 
Then the capacitance is very small, so you can ignore capacitive effects and treat this solely as a resistor.
You're also asked to specifically answer "What does the E-field look like inside the resistor" [emphasis in original]. Therefore any fringe fields that occur outside the resistor are not relevant to the question you've been asked.
