[Grammar] ‘home’ VS ‘at home’

[northpath]

Please indicate which sentences are incorrect or allow both with or without ‘at’ usage.
1. Last weekend we stayed at home because of the rain.
2. I stayed _ home last weekend because of the flu.
3. I think we'll be _ home Saturday afternoon.
4. Call me anytime - I'm always _ home.
5. The whole household was at home that morning.
6. We spent last weekend at home because of the rain.
7. My wife should be _ home now.
8. Oh no! I left my purse at home.
9. At best, we'll be _ home late in the evening.
10 Teresa is not _ home - she's at her sister's now.

I can’t figure out a rule of thumb for that.

And another thing, recently I came across the sentence:
This natural remedy helps insomnia.
No preposition! Is it possible?

 

[Roman55]

1, 2, 3, 4, 5, 7 and 9 are all acceptable with or without 'at', although I would be inclined to use it almost always.

I feel that 6 and 8 require 'at'.

'This natural remedy helps insomnia' is fine. It doesn't actually mean that insomnia is helped by the remedy. It should be seen as a synonym of alleviate.