Does it get any better? Yes....
Does the action get better? Yes, although we do miss out on what sounds like an awesome fight....
Do the characters become more interesting? Yes, well the ones who count anyway....
Does Otonashi get his memory back quickly... Or at all? Yes.... About half way through....
Does the plot become more involved? Yes....
Do the school aspects get downplayed? Well it does at some points.... The school is the setting so it never goes away.... It's play for laughs most of the time and they don't really do the typical school stuff.... The group's aim is to do the opposite of a normal school life....
The show is really good for it's funny bits and it has some tearjerkers.... It's worth a watch.... The first episode wasn't that good so.... Just keep watching....