Q: If I’m playing Solo Cthulhu Fluxx, do I get to draw 3 cards when Cosmic Instructions goes into play?

A: No, you don’t get to draw those extra 3 cards. As a New Rule, Cosmic Instructions is being played during “the turn of the Rules Deck” so it’s not really you who is putting it into play. The Rules Deck, while it acts as a sort of stand-in for human opponents, doesn’t have a hand to draw to, of course, so that part of the card instructions is skipped in the Solo game.