Yeah, both the spawning of new alarm clocks and the snooze durations are randomized. It was a way to get a little more out of the game with a short development time. If I had more time, I'd design it to still be non-deterministic, but more predictable so it's possible to develop strategies.
It is worse to have 5 alarm clocks ringing than just 1, but it's diminishing returns. I ended up using a square-root scaling for the number of alarm clocks that are ringing. So having 4 alarms ringing is twice as bad as having just 1 ringing, 9 alarms ringing is twice as bad as having 4 ringing, etc. Also, having no alarm clocks ringing can recover your sleep, with 1 second of no ringing being the inverse of 2 seconds of one alarm clock ringing.
Having a visual indicator for when the alarm clock goes off next would help with strategy, but feels kind of counter to the intent of the game. When you're trying to sleep in, staring at your clock is kind of counter-productive. As to keeping your hand over it to extend the timer: that was actually kind of a glitch at one point. You could snooze the alarm even when it wasn't alarming, which extended the timer. I ended up fixing that bug before uploading, so it isn't in the game anymore. It could be interesting to have an intentional version of that in the game, though.