When you are negating with not, look at the finite verb in the clause, the one that carries person and tense.
If it is an auxiliary verb (the first verb in a verbal construction) or a form of be, you may simply add not:
He is here. ... The verb is a form of be. >>> He is not here.
He has arrived. ... The verb has is an auxiliary. >>> He has not arrived.
He must have arrived. ... The verb must is an auxiliary. >>> He must not have arrived.
Otherwise, you require DO-support:
He came today. ... The verb came is not an auxiliary. >>> He did not come today.
He arrived today. ... The verb arrived is not an auxiliary. >>> He did not arrive today.
He has a car. ... Here has is not an auxiliary but a lexical verb meaning 'possesses'. >>> He does not have a car.
Until the twentieth century it was common to negate lexical HAVE without DO-support, but this is disappearing. Even earlier any verb might be negated without DO-support, but that died out by the nineteenth century.
Forget "no" and "not" for a second - they seem related, but it is a false comparison.
Instead, think about
"There is" vs. "There is not". These are related expressions but one is positive and one is negative.
Things are simple when the (reflexive) subject of the sentence is expressed positively.
For example, suppose the subject is "life".
There is (life on Mars).
There is not (life on Mars).
The complication is that sometimes the subject is expressed negatively.
Suppose the subject was "no life".
The verb-positive sentence remains the same.
There is (no life on Mars).
The verb-negative sentence has to change, though, because English (unlike Spanish) has rules against double negatives.
It is incorrect to say:
There is not (no life on Mars).
Instead, we say
There is not (any life on Mars).
Other examples of a negative subject becoming positive because the verb is negative:
There is no reason to agree with him. There is not any reason to agree with him.
There is no way out of this situation. There is not a way out of this situation.
There is no one alive who remembers him. There is not anyone alive who remembers him.
In each case, the "not" in "There is not" is part of the verb, making the verb negative, whereas the "no" is part of the subject, making the subject negative. So you can't really compare "there is no" with "there is not" - just remember that in English, you are not allowed to have both the verb and subject expressed negatively.
Best Answer
In your first pair
In your second pair