I've seen other anime where opening sequences are placed much later in the episode, sometimes as far as halfway through. Rarely endings begin a bit early, with a short (cliffhanger) scene following. In Minami-ke Okaeri endings are placed a good third of the episode away from the actual end, acting like a scene breaker. What's up with that? Why such odd timing?
I'd say the late opening is to grab attention and open the viewers mind as to what's going to follow in the rest of the episode without showing an opening which some people may immediately skip if it doesn't seem like their kind of show.
As to the show having more after the ending, I believe its put there as scheme or reward for sticking through the credits, and give people a bit more of the show to finish off.