It's an inevitable part of the ALT classroom experience. The questions that cross the boundary from innocuous to invasive or even offensive and maybe not just to you alone but to others in the class as well. Here's some tips on how to handle these occurrences.
As an ALT, even though you may not technically be a teacher, as a leader in the class it's still part of your job to moderate classroom behavior. Key to leadership is confidence.
Respond with Confidence
If you know what is good and right, your response will be with confidence.
I find it's easy to project confidence in situations like this if you are sure of what is and isn't OK. The students are going to cross boundaries at some point. You just need to know where the boundaries are and you will naturally be sure when correcting the students that it is the right thing to do.
Especially if you are a new ALT in the school, if the students are ever given the opportunity to ask you questions, for example during your self-introduction, their curiosity may slowly lead them to asking some quite invasive questions.
If they are asking in Japanese through the Japanese class teacher, you can expect the teacher will shepherd questions for you. If that isn't the case, simply direct your response to the students and with a grin, deflect the question. "That's a secret."
If the students are asking you directly in English, or the class teacher continues to translate questions you find inappropriate, eventually, you will have to drop the jovial attitude. These inappropriate questions are often a result of momentum so interrupt the mood by showing some of your displeasure on your face. In addition, you'll want to redress the situation and tell that student and everyone "Sorry. That's not a good question." Somber expression and tone is important. But with the next decent question, forgive and forget.
You may find yourself running an activity where students are asking you questions about yourself. It may also be the class teacher or a volunteer student in the hot seat. Students may take this, innocently or not, as an opportunity to ask very personal or inappropriate questions.
If they are asking you, the response explained above works well.
If they are asking the class teacher or a volunteer student, you may have to intervene. One way is to tell the class "Sorry. That's not a good question." as mentioned above before the interviewee has a chance to answer.
Alternatively, you can transfer responsibility to the class teacher and ask them, in a stage voice for the whole class to hear, "Mr. Takamatsu, is that question OK?" If the class teacher says it's not, the class is now being told by two teachers it's not OK.
To discourage further inappropriate questions during a game, remove a point or abstain from awarding a point for that question.
Outside class is probably the hardest time to receive inappropriate questions and your response really depends on the presence you have and the relationship you have with the students.
If the students see you as a friendly, entertaining guest rather than a teacher and role model, you're more likely to get these types of questions. As the old adage goes; Prevention is the best cure.
If you are asked something you find inappropriate outside of class, your response should be depend on the question.
"Do you have a boyfriend?" might be met with raised eyebrows, a surprised but kind tone of voice. "That's private!"
Further questions or something obnoxious should be immediately dressed down but also quickly forgiven and forgotten. A stern "Hey!" followed by a commanding "No." or similar is often enough. Leave the scene then forget about it. Don't hold student's mistakes against them - they are still learning.
We all encounter inappropriate comments or questions in class. How do you deal with it?