I use a 1/4 to 1/8 mono adapter and no issues to report. Not from a synth but guitar pedals etc…
I don’t think that’s a good idea, I think that would short one of the signals to ground,which might be bad(hopefully someone else here might know for sure)
According to @Beefinator its ok and just gets shorted to sleeve(or mixed to mono) with no sound effect.
Mono on the output though is bad.
This rings with Korgs advice with wiring Monotrons -no mono out (but no warning for mono In).
There is no danger in using wrong audio cables. Could be that you only get one channel through it.