Does the law of entropy exclude life beginning any other way but through intervention?

Nope. And life do not break the laws of entropy either. It just seems so sometimes.

The law of entropy has nothing to do with the beginning of life.

Specially trained smart people are trained to determine whether something is alive or not and they very often can't tell. Every now and then a corpse sits up in the morgue or at the funeral. Scientists found a rock they say came from Mars and it has curly something and nobody can be sure if it is a fossil worm, a fossil turd, or just a curly rock.

Technically no - the Earth -- Sun system isn't a closed one. However, that's still a huge chunk of order from chaos to account for.