I watch a fair bit of anime mostly classic era cell shading and hand drawn anime but there are an occasional few modern artstyle anime that have taken my interest as for anime emotes hmmm let's see (White irises with a gaping open mouth and one or two question marks above the head) this indicates comedic shock or bafflement at another characters statement.
(White irises with slight angular brows and some red bruise like marks and a red explanation mark and blush marks) this usually indicates anger and embarrassment towards or of something that another character said about them.
(Star eyes and an open happy mouth) this usually indicates excitement of something or amazement of something, sometimes dreaminess.
(Shades with little stars around a characters face) Usually indicates that someone is trying a bit to hard to be cool.
(Glowing white shades as a person puts there fingertips to there glasses) Often used when a character is being analytical in a kind of mad eccentric sort of way, usually associated with scientist type characters
(Devil horns with a slight shadow over line covering someones face with angular brows and white irises and a curved smile) Usually indicates naughtiness or mischievous intent.
(Black little lines coming from the characters head with black eyelines and tears forming down as there mouth is gaped open) Indicates comical disappointment or rejection.
Most of these and anime emotes in general are used for comedic or over exaggerated social situations but for one of the more serious ones.
(A characters head tilted down slightly as a shadow covers the top half of their face as their mouth is either curved down or even nonexistent) This usually signifies a slow build up of rage in anime sub genres with action and will usually follow with another expression where the character tilts there head back up slightly and a shadow covers most of there face except for one iris although sometimes two where said irises will often be very dilated or there eyes will be smaller than normal, this than usually follows with said character unleashing there hidden power without restraint upon their foe.
The above can also be subverted and played with for instance one scene could bait the audience into thinking it's going to turn dark and gritty only for said character to nonchalantly whip out a comedic emote and act like the whole situation is no big deal, or the reverse situation of what I just described could happen either way it's a good technique if you wanted to catch the audience of guard or keep them guessing.
There are many others but the list would be to long I just googled anime emotes, well I enjoy anime and manga I'll admit it can take a while to get into and understand it's culture especially if your looking at it from a western society perspective as a lot of Japan's eastern society values tend to dominate the genre although I've seen cases where some western society values sneak their way in there.