no/not

Yes, both are OK, and they mean pretty much the same thing.

But there is a rule about "no" and "not"???

Eg. There are no cars BUT There are not (any) cars.

I think we put "no" directly before a noun, while in the case of "not" we usually have to put "something" between not and a noun.

You couldn't say "There is not quiet place", and "There are not cars" is unusual or unnatural in most contexts. However, in sentences such as yours, "not a<noun>" is OK. For example:

There is not a car in the street = There are no cars in the street = There aren't any cars in the street

There is not a hope = There is no hope = There isn

Thanks Mr Wordy.

How about these two? Are both alright?

....but actually it no longer existed.

....but actually it NOT longer existed.

The first is fine; the second is incorrect.

Thanks