何曜日が一番暇ですか？って英語でなんて言うの？

"What day is your schedule free?" This is an informal way of asking your teacher which day they will have the most open classes for you to book. You: "What day is your schedule free?" Teacher: "My schedule is usually free on Thursday." "On what days are you most available?" This is a slightly more formal way to ask your teacher which days they will freer. You: "On what days are you most available?" Teacher: "I'm mostly free on Saturday and Sunday." "I noticed your schedule is pretty tight. On what days are you less busy?" This is a more informal and native English speaking way to ask a teacher when they will have the most open classes. You: "I noticed your schedule is pretty tight. On what days are you less busy?" Teacher: "You're right, my schedule is pretty full. However, I'm usually less busy on Tuesday."

In this example, you are specifying 'lessons' at the end of the sentence to show that you specifically want to know the teachers availability for classes.

"What's your schedule looking like tomorrow?" this asks the teacher to explain how busy they are or how many spaces there are when you may book a lesson. If your teacher is very busy, you may ask, "Do you have any gaps in your diary for tomorrow?" to identify when would be a mutually convenient time for the lesson. "Do you have any gaps in your diary for tomorrow?" "Yes, I'm free between 3 and 4pm."

This means you want to know the day the teacher will be available.

"When are you free in your schedule?" - In this question are are asking your teacher when is he/she free for a lesson, when asking this question aren't being specific whereas if you ask "Which days are you available for lessons?" - You will be more specific, asking your teacher which days he/she has open slots for you to book the next lesson. I want to book another lesson with you, which days are you not as busy? - In this sentence your question is direct and specific. You are stating the reason you are asking the question as well as finding out the exact days/dates that your teacher will be available for you to reserve the next lesson.

Teachers, just like anyone else, do have other commitments to attend to. Some of these commitments may be routine and planned for well in advance. For the ones that will have been planned for well in advance, a detailed slot availability will be visible on the teacher's website. The impromptu ones may be difficult to disclose to the student when asked these questions because they are unforeseen. However, you may ask as follows: On which days and times are you mostly available for bookings? or Which are the best days and times for classes on your schedule?

The first question, "When are you next available for lessons?" asks the teacher when they are free to teach you. It specifically asks for the soonest possible time that they will be able to give you a lesson. The second question, "When is a good time for you to teach me?" is a similar questions and will get a similar response. You are just using different grammatical tools. I hope this helps.

When are you available? When suits you? What is your schedule for next week? Are you busy next week? I'd like to book multiple lessons. All of these are okay when trying to find out what days the teacher will be teaching.

"What day's are you free to teach me?'' can be said when asking a teacher when they are free to give you some lessons.

Sometimes trying to book with a teacher can be hard if they are popular so you might want to know if they have any quieter days so you can make sure you can get a lesson booked you would ask 'What days are you most available?' or 'What days are you mostly free?'

"On which day are you available?"is asked when somebody wants to make arrangements with you but before doing that they would like to know when exactly you are available so that they can let you know about their specific arrangements in advance.