This is all true. Stern talk is certainly helpful... to a point. Be aware that he is listening and absorbing everything, and since your rules are literally his entire world, he will be the most amazing rules lawyer possible. And he is way smarter than you think way younger. At 3 my kid was reprimanding my behavior for not following my own rules, and lately he's begun to tell me when I've been unreasonably angry ("you need to listen" or "you yelled and made me sad" are the forms this sometimes take... just apply judgment as to whether he's correct so he doesn't take advantage of parental guilt). He's sometimes mixed up about cause and effect (he's 3) but taking his emotions and 3 year old logic seriously has been very helpful for understanding why he's upset and helping him control himself, or tell me when I've been acting unreasonably.

Also, Daniel Tiger is amazing. There's a song for everything and he's memorized all of them.