Flash alerts cause the screen to flash when a sound alert is played, and make these audio alerts accessible if you have a hearing impairment.
Mono audio simply means that the left and right earphones play the same audio, without any stereo effect. This can be useful if you have better hearing in one ear than the other as the same sound is sent to both earphones. Without this setting enabled, you may find that certain sounds get sent to one ear or the other which may make some content difficult to understand.