5. I don't think we have anything like Monty Python's Flying Circus.
Britain has a plethora of sketch comedy groups, many of which have been given their own TV shows, but yeah, I can't remember ever seeing anything similar on American TV. Saturday Night Live seems to be the closest you have, although the cast is constantly changing on that, it does feature a fair bit of absurdist comedy though.
Kids in the Hall remind me a lot of Python, although they are Canadian of course.
My favorite right now is Key & Peele on Comedy Channel. It's more understated but Portlandia on IFC is sketch comedy. In thr past there was In Living Color, Chapelle, The State, probably others I'm missing I'm sure.
EDIT Guy beat me to it here