I have to ask my friend "In what time the class it will start tomorrow". My question is if the using of "In which time the class will start tomorrow" is correct as well.
The correct usage is "At what time will the class start tomorrow?"
You could also say "When does the class start tomorrow?" That is more colloquial. "At what time..." is more correct but a little formal. You can also say "At what hour..." but that is rather old-fashioned now.
"In what time" is used to query duration. For example: "In what time can you run a mile?", i.e. "How long does it take you to run a mile?"