While using shape-builder tool I always have this problem with lines looking like they fit together perfectly but in fact they're not. Is there a way to snap line to line without zooming so far?
Two lines or curves can be put to exactly same place only if they are identical (= have same form, size and orientation). There's not available any magnet which sucks one already existing curve or line exactly along another already existing shape if the difference is small enough. It must be zero if you want to align two shapes exactly.
If you want 2 identical pieces in the same place, you get it most easily by duplicating (=copy, paste in place). You can also draw with some snapping mode ON. Be sure that you have only one snapping in use. I recommend Snap to points. Drawing works well only with straight lines. Even circles snap in rare cases (=smart quides =ON, nothing else tries to catch the snap)
If you are going to create new shapes with shape builder, consider also Live Paint. It does not delete the originals. You do not need duplicates. The difference is that you must expand the object to make the created shapes independent.