I'm confused "home" and "house" also the preposition "in" and "at" before them, for instance
1. Where's your daughter?
She is at/in her friend's house/home
2. There's no air-conditioner in/at my house/home.
Which are correct?

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“Home” is used in a more personal way than “house”. The prepositions “in” and “at” depends on what you are trying to say.

1. Where’s your daughter?
She is at her friend’s house.

You use “at” when you or another person is visiting a place. Another example would be “I am at the park.”
Since you’re talking about her friend, you would use “house” rather than “home”.

2. There’s no air-conditioner in my house.

You use “in” because the air-conditioner is inside your house.
For this sentence, you can use “house” or “home”, but it depends on the way the sentence is said. If you wanted to use “home”, you would say “My home doesn’t have an air-conditioner.”

I hope this helps!