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Dear teachers, I wonder whether the judgements of the following sentences, referring to any, are right or not.

Doesn't anyone know the answer?

Does anyone not know the answer?

No one believes me.

Does no one believe me?

Doesn't anyone believe me?

*I won't see any person / anyone, who has not made an appointment.

I won't see some person / someone, who has not made an appointment.

* Anyone doesn't listen to me.

Someone doesn't listen to me.

No one listens to me.

*Anyone is not allowed to go out tonight.

No one is allowed to go out tonight.

*Any one of us doesn't have any money.

None of us have any money.

No one who knows her thinks she's anti-military...

Anyone who knows her doesn't think she's anti-military...

No one who comes in here leaves alone.

Anyone who comes in here doesn't leave alone.

In a word, we can say "no" instead of "any not", or contrastingly "some". On the other hand, we can say "anyone" meaning "any person at all, it doesn't matter who".

Could you please correct my mistakes, if any?

Oh, so many questions. I'd appreciate your kind help.
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These are no good; the rest seem passable to me in at least certain situations:

Anyone doesn't listen to me.
Anyone is not allowed to go out tonight.
Any one of us doesn't have any money.
Anyone who knows her doesn't think she's anti-military.
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I'd just like to add to Mr M's comment that any cannot be the subject of a clause and be followed by not. If any, anything or anyone is the subject or part of the subject, the clause is always affirmative:

Anyone can do it. Wrong: Anyone can't do it. You have to say: No one can do it.

CB