Installing engineered hardwood to exposed edges
All edges need to be concealed by trim, whether it's baseboard, base shoe, transition strip, or termination molding. 

In most of the cases you mentioned, a simple L-molding should do, such as against the stair railing board. Obviously your stairs are getting some new treatment or other, so that could serve as the overlay. 

Consider cutting channels under your stone with an appropriate saw so your flooring can slip beneath it. This would be the most professional and aesthetically-pleasing solution.