Q: What do the world's major cities look like? Do they still exist?
A: The world's cities have, in large part, been abandoned; some people may choose to live in the ruins, but most of the populace has chosen to reclaim smaller villages and towns due to the fact that they're easier to manage and defend. To get an idea of what major cities look like at the current time, run an image search for Life After People. Urban decay has taken hold and structures have become largely overgrown with vegetation.
Q: Does a mage's familiar need to eat/sleep/use bodily functions?
A: Yes; a familiar functions as the same animal whose form it has taken. A hawk will hunt mice and birds, a seal will eat fish, a deer will graze, a wildcat or wolf may spend time away, finding bigger game such as rabbits, grouse, and young deer. If one can afford it, a mage may choose to offer to feed them as they might a regular companion creature.