What happens to the side information (L-R) when mix is summed to mono? Is it removed and disappears completely or is it blended to the center so we can still hear things that previously made a stero image but now are in center and not in the left/right sides (obviously, because it's mono)?.
In short, so long as the two sides are not out of phase, then you will hear everything that was on the hard left or right at the same volume, but all now in the centre.
The 'same volume' however, depends on the pan law used when summing.
Most apps use a standard pan law of 6dB, which ought to equate to 'the same volume'. Some have an adjustable pan law so you can change how the summing is perceived in the final mono file.
If your left & right were the same signal, but out of phase, then they will add to zero... silence.
This could happen if you were trying to use a mid-side process on an artificially generated signal.
At the signal level, a stereo mix is all side information. The 'centre' sensation is just an illusion caused by being able to hear the same thing (or similar things) in the L and R channel. (To be fair, that's how our ears work too - most of us don't have a centre ear).
So when an L-R mix is summed to mono, everything is blended to the centre, and in general, in the mono mix you will still things that were in the L channel or R channel only.
The only time when things wil disappear will be if they were originally in the L and R channels, but those signals were out-of-phase with each other. If this happens, both those signals will cancel each other out when the L and R channels are summed. It's a bit like adding a positive number to a negative number: (-9) + (9) = zero!
You might also experience this effect happening partially if the signals in the left and right are slightly time-shifted, as might happen if you passed them through some stereo effect. When summed to mono some parts of the frequency spectrum might disappear, giving a filtered version of the original sound.
Summing stereo signals to mono can result in problems like certain frequencies coming from a certain direction being disproportionally attenuated. For stereo signals intended to be usable in mono contexts (like radio), there are special recording techniques (like M-S microphoning and recording and to a lesser degree X-Y microphoning that tries to minimize phase differences).
Tracks that have been created by panning mono sources by volume (without using delay or other more sophisticated stereophonic effects) are also mostly unproblematic (see below) but that's more of a sixties/seventies style of doing things.
Identical but panned signals end up adding their amplitude, unrelated signals end up adding their energy so in a mono mix of the "panned mono signal" variety, the center signals appear stronger than in a stereo reproduction. Which is often ok since the mix tends to put the singers/solo there.
Independent signals with basically identical content (singers, guitars, pianos) add their energies. Problematic are instruments with highly constant frequencies and comparatively pure tones: some organ registers, glockenspiels, a few other things. Mixing those will result in distracting beatings of slow speed.