Does anyone know exactly how the in game timer works? Does it pause between levels? Say I get perfect, I have to wait an extra second or so for the guy to say "Perfect!" does that extra second or so add on to my overall time?

You can ask for the developers pf the game on discord.

I don't think so, losing a stock most likely takes more time but i can check

"Perfect!" takes around 1.5 seconds meanwhile losing a stock instantly takes around 2 seconds so even if you die instantly it is still better to "perfect" it.