These questions are basically the same; however, the 2 that contain "will you be home" are used most often in situations where you want to know when the person, who has been gone all day, will come home (after work, school, etc.). The other 2 questions (with "at home") are often used when the person has a changing schedule and is going back and forth between home and doing errands or taking a class. I hope this isn't too confusing. By the way, another comment: Starting a sentence with "At what time..." sounds rather formal for conversation. We'd almost always just say "What time...".