This is hard as a lot of these uses are not about 'house' in its most common basic meaning. Do you mean how well they explain the concept of house 'the building'. some of them don't explain that at all. But if you just want a rating of how natural the sentences sound (with all the various meanings of house) here are my ratings. I'm from the UK and speak British English.
I live in a house near the beach. 4
On rainy days, we like to build a house of cards. 4
After he had confessed, he was put into the house of detention. 2 (house of detention not really British English, we'd say prison).
The priest looked very angry when someone shouted in the House of God. 3 (again, not a commonly used phrase, we'd say church).
How many people live in your household? 4
His plan for his new business was like a house of cards. 2 (poor use of the metaphor I think/ cliched).
They move house before the fight with the neighbours will get out of hand. 1. Ungrammatical. As well as Feebs's examples: They will move house before the fight gets out of hand -
After my sister had read my diary, my parents gave her house arrest. 1 'gave her house arrest' ungrammatical. People are put under house arrest, not given it. But I agree with feebs that 'grounded' is the appropriate term.
The old woman lived in a houseful of cats. 2 I'd say with a houseful of cats.
We had to lower our household budget when I lost my job. 3
The house rules were short and clear to everyone. 2. The list of rules might be short but not the rules themselves.
We save our breadcrumbs for the house sparrow.4
He tries to sell his products house-to-house. 2 As feebs said, door to door.
Because of the housing shortage, I could not get my own house and had to live with my
parents again. 4
He was so happy that he could shout from the housetops that he had graduated. 4
After having been a housewife for years, she decided to study Law at university.4
The house wine was one of the best wines I had ever tasted. 4
The housekeeping money was gone after my brother’s girlfriend left. 3. A bit unclear at first. Can't help reading it as 'gone after'.
My friend has bought a house boat with his brother.4
After I had broken my leg, I was housebound. 4
The housing market is experiencing a cooling-off period from the boom several years ago. 3. after the boom.
He gets up at six and disturbs the whole house.4
The old man was housed near his children. 2. Sounds a bit strange. 'Housed' is very passive sounding, as though he were put there with no choice.
I always keep house before my parents come to visit me. 1. 'Keep house' not British English for cleaning/tidying.