Yes, it is always good to have a little bit of a slope, so that any moisture on the BB or Inner Cover will flow to the outter edge of the hive.
That seems really close to the neighbors door. I would go talk to him to be sure he's ok with it and let him know what you are doing. He will get lots of bees up there, I'm sure. Make the first move to be proactive of any potential problems, that way he will be more understanding if a true problem develops. The days you inspect and when you install bees, there will be bees all around that door. Depending on how you handle them, they may be itching for a fight, and sting people walking around there.
OH, and promise him some honey :D Good luck.