Actually, Madoka didn't sacrifice herself. Think of it this way: her existence transcended flesh and blood, specifically due to the premise of her wish. Can you physically be in multiple locations simultaneously at any given time? Can you exist where you are right now and also exist in the middle of Europe tomorrow at 13:40 GMT? No. That's impossible- physically impossible. Therefore, for her wish to be (literally) everywhere, her being cannot exist in a physical form, but that doesn't mean she's straight-up "dead" per se.
You got half the cycle of witches and witch hunters thought out. The universe will naturally always have both. However, instead of having witch hunters, she will replace all of them. To put that in an analogy, if there's a police force of 1000 men and 1000 burglars out on the loose. Madoka alone exceeds the force of those 1000 men and can take out all 1000 burglars.
They didn't travel to another timeline. Or at least, I don't recall there being a suggestion that there was. Only Homura does the time-traveling, and only Madoka was capable of vanishing that witch. To the main characters, the storm that brewed was the incoming witch. To all the non-witch hunters, it was merely just a huge storm to them. Therefore, with the witch wiped out, the storm's gone, and everyone's back with normal days with regular forecast. How Madoka's brother remembers her name is like a plot device that involves memory loss and one person living to tell the tale. I don't have a solid explanation for it, I've seen stuff like this often enough that I can accept it.
And yes, dad's a stay-at-home.
