I'm not overly familiar with the technology, but it looks like Hawkeye only creates a 3D model/prediction for goal-line decisions (did the ball cross the line). The other decisions appear to be based purely on replays of different camera angles.
Multiple calibrated cameras for the 3D offside tech (3D being the system shows the vertical line on the crosshair).
The positions of various points are calibrated in advance allowing the lines to be plotted accurately. Angle of the camera etc isn't an issue except where a relevant body part is obscured, whereby they switch to an alternative calibrated camera.
Hawkeye and FIFA have a few videos kicking around, it's clever tech and I suspect a lot more accurate than people initially give it credit for.