You are correct on (2), but there is nothing to stop a sound system from emitting a controlled set of sounds, recording them with mikes, and calculating
Some modern audio systems have tried to implement such systems as you describe here, however, this only solves a very limited range of issues -- specifically, issues involving amplitude of a particular frequency. Yes, a sound system can emit a controlled sound and compensate for a particular frequency being louder than the others (this is basically an automatic EQ), however, a speaker cannot compensate for reverberation times or delayed reflections.
Remember that any room will have some amount of reverberation, and that reverberation is not always constant across the frequency spectrum. For example, you may hear a longer sustain for low frequencies than you do for high frequencies. Or perhaps, you have one particular frequency that tends to sustain a bit longer than the others. Reducing the amplitude of that particular frequency does not change the reverberation time. In fact, the amplitude of that frequency may be correct volume wise and reducing it would cause your sound to be even less balanced. There is no way to fix this without modifying the physical parameters of the room itself.
The other issue is called "early reflections". The idea here is that you have sound reflecting off of another surface which arrives at your ear later, most likely causing a stereo imbalance or phase issues at certain frequencies. For example, your right speaker projects sound toward you, but some of it reflects off of the left wall and then arrives at your left ear a split second later. Now your stereo field is incorrect and you have possible phase cancellations for certain frequencies. Again, the only way to correct for this issue is to stop the reflections by treating the room, an audio system cannot compensate for this.
Serving coffee on aircraft causes turbulence.