How do I remove all the lines when I make a square? I think it's some setting I've messed up.

Camilla,

as Ton mentioned, it is a regular functionality when the Tilde key is pressed (or some other key depending on what international version of Illustrator you are using).

On rare occasions the mass duplication may also happen for some unknown reasons. In that case, quitting and restarting Illustrator usually solves the issue.