Learn English – What preposition should be used in “the conversation has been driven […] the subject”

"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".