Kinda makes sense. When you are not connected you should have a lower ping. If you get a high one when you are not connected then you should get your computer checked. Not a bug.
This is not a bug. If you READ you can find out what is actually in minecraft.
Zombies aren't supposed to shoot with bows. It's not a bug. Make sure you know it is a bug not something you think the game should have before posting.
The /ban command does not use a duration parameter because it has not been added.