From this data, we can calculate what momentum the electron had when it was passing through the hole.
We can't do this. It is true that in principle, we can measure all three components of momentum $p_x,p_y,p_z$ with arbitrary precision at single time, but in general, we do not know how to extrapolate this to past to find "particle's components of momentum" at some known previous time or assign momentum to some region of space ("hole in the wall").
We can do naive extrapolation by assuming that momentum did not change at all, so the particle always had the momentum we measured. But this is unphysical, because we know the particle had to interact with the wall, and with other bodies before that. So this naive extrapolation is good only for limited span of time/region of space where interaction is believed to be negligible.
So we can know the electron's position (as it was inside the hole) with arbitrary accuracy and also simultaneously know its momentum.
No, because we can't extrapolate the momentum measurement back to time when the particle was "inside the hole", and also we do not know exactly where the particle is when we find its momentum, so we can't just draw a line from "position of particle when its momentum was measured"; there is no such single point.