Yes, it's gender. The -in- makes it explicitly feminine (amikino), and you can use -iĉ- to make it explicitly masculine (amikiĉo). Amiko does not specify the gender.
Because ĉu is for yes or no type or a choice between two things not an open ended type question. You would use it if you asked do you live in Europe? Or if you asked do you live in Europe or the United States?