Use the protractor tool, start it at a face1 edge and make the guide line at 90 degrees. Rotate the second object about this point and snap to the 90 degree guide line...

You can change the axes (Tools menu > Axes) but the align view will always be related to the original world axes. If you "set up" your building however correctly, this generally doesn't cause a problem because the view will still be somewhat "natural".

Perhaps it wasn't a typo.

You can do it pretty quickly by just doing a right to left selection across the top of the push pulled object and hitting delete