Also, I've noticed that closed questions get hidden eventually. Does this just happen when some mod decides to do it, or do closed questions get automatically hidden when they're old?
The reason we close posts before hiding them is so the asker has time to respond and other people can see what happened to the post before it disappears. Usually we give two days but it can be shorter or longer depending on the circumstances.
Otherwise I'm not sure what you mean by "How long does it take for a post to get old?" Old relative to what?