The first sentence infers that by offering a poacher (someone who traps animals for food illegally, usually on private land) a rabbit stew, you are in fact encouraging him - poachers often catch rabbits which they sell for food.
The sceond sentence is more likely a joking warning that the child may become a victim of a witch's spell, and actually be turned into a frog - the amphibious animal. The warning would not be meant to be taken literally - just a jokey way of stopping the child doing something he shouldn't.
Yes, it does mean serious - probably while the temptation was to laugh, or at least smile, but keeping a 'straight face' means giving nothing of the person's reaction away in their facial expression.