What is 3 crimes and the punishments that the puritains might witness?

There is, of course, Hester's punishment for adultery. This gets her an embroidered "A" embroidered on her chest plus a period of being shunned.

People were banished for saying things against Puritan law.

People were also forced to mount a scaffold and confess their sins.

Although it did not happen in this novel, people could be killed if they were thought to be pals with the Devil (check out The Crucible)