Great topic and something I'm always interested in.
My cats are great at communicating their wants. Maybe they think I'm dense and need all that help, lol. Crystal meows and stretches up and makes eye contact when she really wants something, like tuna. If Russet wants to be petted, he will jump up on the bench and sit next to me, and just kind of lean into me, letting his shoulder bump me hard. He does it over and over, lol. Bring a toy and drop it if they want to play. Run away (or across my path) with a fussed-up tail in the shape of a question mark if they want to be chased in play. They have a whole set of language for the dog too, to solicit attention or play from him, or tell him to back off.
As far as mood ... Crystal gets what I call "witchy". It's hard to describe because I see it in totality, but it's mostly an expression in her eyes that I will notice first. They are slightly narrowed. She may or may not lash her tail, or make an annoyed growly sound, after someone approaches her when she is in this mood. She may also swipe a paw, or in the case of Russet or the dog just make a sudden leaping attack. She expects everyone to know when not to touch her. She may even roll on her back, but she does NOT want her belly touched when she's in that mood. Most of the time she adores full body scratching and rubbing and wants a tummy rub, but not then. That's the only time she will get rough with me, if I touch her belly when she's like that. She will bite (not breaking skin though) and may grab and hold with her claws.
The ears are sometimes involved (turned back) but again, like the tail lashand growl, that comes AFTER you've offended her in that mood.
When Russet is upset, he's easy. His pupils get big, and he jumps down and away, giving a certain two-syllable "me-OWWWW!" as he lands, and hops away. If I walk in his direction he will leave, keeping distance between us, so that is that. It's similarto when he is afraid(?) because I fuss at him and he leaves, but that's slightly more wild-eyed and the ears are back more. I don't see tail lashing from him as a sign of annoyance. He doesn't lash his tail. Too lazy probably, lol. Unless he sees a bird or squirrel outside.