Things I don't understand, vol. II

Phrases I don't understand, never have, have even heard used in conversation, in context, and still have no idea what they mean:

"Throwing the baby out with the bathwater" I'm more farmiler with the cultural background of this idiom than the actual meaning.

"Proof is in the pudding" No idea

"Don't look a gift horse in the mouth" I had to look this one up to wrap my head around it, why would you look a horse in the mouth anyway? Dad, I'm looking to you on this one.

"Don't get your nose out of joint" Seriously, that's just random words strung together.