Are you serious OP? You're smart, I'm sure you know the bulk of the answers already.
You're not trying to get us to answer a film school assignment you have, are you?
Anyway...
What plot points and characters are audiences expected to understand just from the genre of the film for the different genres?
I think this is a a pointless question. Just write the best script you can. If you direct, then direct the best movie you can.
The answer is one that I'm sure you already know - there is no one answer. There can be a great variance between movies of the same genre. Sure there is an average and I'm sure you already know what that is.
But the variance exists and is key...
There are thought-provoking and smart comedies that require the audience to think and understand complex story lines and plot points: some Woody Allen moves being good examples.
And there are comedies that require little to no thinking by the audience (and consequently have easy-to-understand story lines and plot points)- The Hangover etc being examples of that.
Ditto for dramas, thrillers, even some action movies.
For complex see Momento, Matchstick Men, Upstream Color, Inception, Donnie Darko, Brick etc. Can you still enjoy these movies without understanding all the twists and turns? Yes... But it's damn rewarding if you work out what is going on.
For non-complex requiring little to no audience thought processing - see the majority of Hollywood's blockbusters.
What are the rules to the genres in genre film?
Ask your professors at film school. Do I have the hours required to answer this? No.
Do I think it worthwhile to you or others to answer this? No.
Be aware that the best movies often bend or break some genre rules.