at/in the student's house/home

I will teach [color=red]in the student’s [color=red]house.
I will teach [color=red]at the student’s [color=red]house.
I will teach [color=red]in the student’s [color=red]home.
I will teach [color=red]at the student’s [color=red]home.

Hello,
I am confused. Would you please be kind enough to tell me which one is incorrect and which one is correct?

Thank you

I am confused. Would you please be kind enough to tell me which one is incorrect and which one is correct? [color=blue]They all can be correct, but the last one is least likely.
This is a difficult topic and it is unlikely that all your confusion will be erased by my first answer. One confusing factor is that sometimes ‘home’ is used to mean ‘house’, but the correct meanings are as below.

A person’s home is the place the person lives (in)(at).
A house is a single building of variable size in which usually one family lives.
People who don’t live in single-family houses usually live in apartment buildings, which are large buildings that have many small units within them, called apartments, that one or more people or a family lives in.
Some people don’t live in houses or apartments. They may live in tents, trailers, house boats, etc. But wherever they live, that is their home.

If you live in a house, you can be at home but still not be in the house. You could be in the yard that usually surrounds a house or you could be sitting on the front steps of the house or be on the patio behind the house.
If you live in an apartment and are in the apartment, you are at home.

I’ll stop here and wait for you to ask some questions.