Yes, 'mixed' is usually used to refer to a team or a class where both genders are represented (except in the case of the phrase 'mixed marriage). Otherwise, we would say 'a combined team' a 'combined class', meaning that the it was made up of people who differ in some other way - apart from gender. So a class made up of children from grade 3 and grade 4 would be 'a combined class'. A football team made up of players from several different teams would be 'a combined team'. When the term 'mixed marriage' is used (if indeed it still is), it refers to a couple with different racial or religious backgrounds, I suppose because up until now the fact that they are opposite genders is a given. Of course that may change given the move in some places to redefine marriage - it will be interesting to see how the language evolves to reflect changes in society.

It depends on the context.In tennis, for example it is called mixed doubles (each team has a man and a woman playing) . In school the youngest classes were called "mixed infants" when I was very small. So yes, usually the term mixed is used.