It's correct because it's a diminutive. The '..chen' suffix, meaning little, makes the noun neuter. It doesn't make the person referred to any less feminine/female!

Hola Jorge, no, "Mädchen" es neutro. Eso es una diferencia entre aleman y español. Tenemos tres formas: masculino, femenino y neutro. Y en caso de "Mädchen" la forma correcta es "das Mädchen". Eso es algo que hispanohablantes deben aprender ;-)

There is no general rule in German about which noun gets which article. However, there are a few words where you can deduct the article from the noun: http://www.deutschegrammatik20.de/das-substantiv-nomen/genus-artikel/regelmaessiges-genus-regelmaessige-artikel/ This gives you a short overview. In general, I would recommend to learn the article with every new noun that you learn. (So don't learn just "Baum", learn "der Baum".) You cannot underestimate the importance of the article in German, it's the basis for every sentence and every adjective ending, so please make sure to memorize them from the beginning! You will have huge advantages later on if you know your articles. :)