Yes, BOM cost etc is lower, fewer parts.
Yes. The idea of balanced connections is a) to have impedance symmetry and, more importantly, b) to avoid "GND balancing currents" between gear to develop an error voltage in the cable (yep, the classic ground loop issue). Signal symmetry is not required but it makes sense to do that as well as then the output voltage can be quite large even with low supply voltage like +-5V. You cannot swing 4Vrms (which means +-5.7Vpeak) with 5V supplies.
No. Shorting one of the output lines is only allowed with true floating transformer output or their electronic equivalent, the servo-balanced output. When you short one line to GND with these, the other line automatically doubles its output voltage so that the net difference is the same.