shouldn't

[Anonymous]

Hi,
Would you please check these sentences and correct them for me?
1. Shouldn't you help your mom?
2. Shouldn't you knock first?
3. Can you give me one good reason why I shouldn't arrest you?
4. Shouldn't you be studying for your finals?
5. What are you doing here? Shouldn't you be at the hospital(,) looking after your patients? [This is correct with the comma, isn't it?]
6. Shouldn't we have called the police?
7. Are you feeling ill, Mom? / There's nothing to worry about, my darling. You shouldn't worry. Just a little flu. [Here, is 'shouldn't' used correctly? If so, what's meaning? - In my humble thought, it should be "You needn't worry."]
Thanks in advance.
Have a good day.

[Rusty]

1. Shouldn't you help your mom? (OK).
2. Shouldn't you knock first? (OK).
3. Can you give me one good reason why I shouldn't arrest you? (OK).
4. Shouldn't you be studying for your finals? (OK).
5. What are you doing here? Shouldn't you be at the hospital(,) looking after your patients? [This is correct with the comma, isn't it?](I don't think the comma is necessary. The sentence is OK).
6. Shouldn't we have called the police? (OK).
7. Are you feeling ill, Mom? / There's nothing to worry about, my darling. You shouldn't worry. Just a little flu. [Here, is 'shouldn't' used correctly? If so, what's meaning? - In my humble thought, it should be "You needn't worry."]
(Both are OK. "Shouldn't" means "ought not." "Needn't" means there is no need to worry).