A baby snake is called a hatchling (from eggs) or neonate (live-born). Fully independent from birth — no mother needed.
Yes — venomous snake hatchlings are born with full venom. In fact, some baby snakes produce more potent venom than adults (though they inject less volume). Never handle a baby snake you can't identify.
Born fully independent — no parental care needed
Venomous babies have full venom from day one
Copperhead babies have bright yellow tail tips to lure prey
Rattlesnake babies are born with one "button" rattle
Baby king snakes are immune to venom — eat other baby snakes
Some baby snakes are born live (boas, anacondas)
Anacondas can give birth to 40+ babies at once
Hognose babies play dead with the same drama as adults