Pronouns

Karan thinks "aap" is only used for multiple people, never for one single person alone. So when he speaks to his teacher one-on-one, he says "tum". His mother says "aap" is correct for a teacher. Who is right?

A strange object is on the table. Tanya asks "yeh kaun hai?" (who is this?), trying to find out what the object is. Her friend says "kaun" is the wrong word here. Who is right?

Ishita thinks there is no real difference between "tu" and "tum", both are similar, "tu" just sounds a bit old-fashioned. So she says to her grandmother, "tu kahaan ja rahi hai?" Her mother gets upset. Is Ishita's thinking correct?

There was a knock at the door. Sameer says "kuchh aaya hai" (something has come), meaning to say that a person is standing outside. His sister says the word "koi" should be used here. Who is right?