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.
"Of" and "on" can both be used, but they have slightly different meanings and usage:
First, when asking people for ideas, it is common to say "Do you have an idea of (something)", but usually when using "on" it is more common to say "Do you have any ideas on (something)".
"an idea of (something)" means that the idea is an answer to the question "what is (something)?" or "what do you know about (something)?":
Do you have an idea of his current location?
(The desired "idea" would be something that answers the specific question "what is his current location?")
On the other hand, "an idea on (topic)" means that the idea is about a particular topic or area of thought ("on" is basically a synonym for "about" here):
Do you have any ideas on Hegelian Philosophy?
(The desired "idea" is something about "Hegelian Philosophy", but the question here is more "what do you think about it?" not "what is it?")
Now, when the thing you're asking about is phrased in the form of a question, technically either one can work:
Do you have an idea of what I should do?
(what is the answer to the question "what should I do?")
Do you have any ideas on what I should do?
(what do you think about the subject of "what I should do"?)
In many cases, they have more or less the same meaning, though using "of" can imply more that you want a single, complete answer to the question ("You should do homework"), while using "on" can imply that you don't necessarily expect a complete answer, just any information or thoughts would be helpful ("well, I think doing homework would probably be a good idea, but watching TV would definitely be more fun.")
For your second set of examples:
I have a rough idea on what you're talking about.
This says you have an idea that is related to the thing that's being talked about (e.g. "I have an idea for how to make that thing better", or some such).
I have a rough idea of what you're talking about.
This says that you have a rough understanding of the thing being talked about.
So they are really not equivalent in that case. Basically, if you can replace "idea on" with "idea about" and it still makes sense (and says what you intended), then it's probably correct usage. If it doesn't, then you probably should use "of".
Best Answer
In all your examples only one sentence is correct every time. "Is" is a main verb there. That means we translate it and it is the only verb in the sentence. For example:
There is no other verb besides is, and this sentence is correct.
"Do" is not a main verb, it is used to make negatives and questions. There is always another verb in the sentence, which we translate. All the other sentences are examples of that; the verbs are: practice (first example), come (third example), matter (fourth example), care (fifth example), realize (sixth example).