The tablets in my OTC jar are 10mg, and they're pretty small already, not easily divisible, and certainly not to 1/100th of a dose as the sibling comment is suggesting. This is an interesting suggestion though, maybe I'll try just licking one some night and see if that has a noticeable positive effect sans the downsides.
Pretty much all the melatonin in physical stores is hilariously overdosed, yes. If you're in the U.S., you'll have to look for products from specialty supplement brands. I take a tiny 300mcg capsule.
This. Try with smaller doses starting from 0.1 mg (liquids are best for this) and work your way upwards to reach the optimal dosage. Tablets are often overdosed which leaves you drowsy in the morning.