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Well then that shouldn't be a problem so long as the power for both rooms is on the same mains phase. If it's not... Things could get nasty. Same if there are differences in earth potential between...

Simple answer : quite a few.

Be careful of creating ground loops though, especially if speakers you put on the line level chain are powered from different mains wall outlets.

The question here...

If one is powered off, then maybe not but it depends on the makeup of its guts. Otherwise yes.

The technical explanation of why you shouldn't just combine the outputs of audio devices is this :

The output impedance of a mixer or other playout device is generally quite low, say around 150...

Blah blah output impedance blah blah input impedance..

Or in laymans terms...

Ye cannae just combine mixer outputs into one cap'n or she's gonna blow.

Better to use a passive or active...