The bottle is filled with a flammable liquid usually something thick like motor oil or diesel, and stoppered with a cork or cap, then a rag is tied around the neck of the bottle, not stuffed into it. Then the rag is lit, and the bottle thrown. When it hits, it’ll break and the lit rag ignites the fuel in the bottle.
This is of course purely talking about the historical use of these devices. I definitely don’t condone anyone saving their wine bottles and corks for future reuse.
Alchemist's Fire is basically the Molotov Cocktail of 5e, so I'd just use that.
1d4 Fire damage per round unless they take an action to put the fire out seems pretty reasonable to me. Puts it on par with a shortsword at the very least.
Fireball's damage is insane (the designers intentionally made it deal more damage than spells of the same level "because it's an iconic spell"), so I wouldn't really use it as a baseline for balancing anything, personally.
Alchemist's Fire also exists in 2.0, 2.5, 3.0, and 3.5. I dunno about WoW with dice 4th edition, or 1st edition. My parents had both the red and blue boxes, but we read the rules and immediately went for AD&D cause that was more flexible when we started the family game in Dragonlance.