Talk or speak

Hi Pieanne,

No, no formal rule. The words occur in different situations: for instance, I speak at a fundraising dinner and then talk to my friends afterwards. Usually, either one is OK. Speaking is perhaps a slightly more formal use of the voice in communication. Making a speech is a more formal activity than giving a talk.

do we say "talk to me" or "speak to me" then?

or

is speak one-sided, while talk is "two- or multi-sided"?

Within the context you have given, both are equally possible:

'Talk/speak to me, darling!' -- both are fine.
'They were speaking/talking to each other when I entered the room' -- both are fine.
'Everyone was speaking/talking at once, so I could not make myself heard' -- both are fine.

Did you attempt to make some sample sentences for yourself before posting, Seyfihoca

Yet, you say: "speak up", "speak"different languages, "talk one's way out of sth", "it's just talk!" I take it is a matter of idioms, then?

from Cambridge;

-Would you mind speaking more slowly, please?
-"Can I speak to/with Ian please?" "Speaking!"
-If he tells Julie what I said, I'll never speak to him again.
-She spoke of her sadness over her father's death.
-She speaks very highly of the new director.
-I can certainly come but I can't speak for my wife.
-Who is going to speak for the accused

Yes, many are just a matter of idiomatic usage and stock phraseology.

I said nothing previously about your sentences, Seyf, but the ones in which 'talk' sounds awkward seem like set phrases to me: 'speaking as/of', 'speak for', 'speak highly of'. If you wish, you can make a list of these and call it a rule-- and another rule for 'talk one's way out of'', 'talk turkey', 'talk someone in

apart from idiomatic use, is it right to think that "speak" means "uttering words", and "talk" "have a conversation"? (on the whole)

that sounds more comprehensible.

is "speech" a derivative of "speak" then?

Yes, it's the same root

we say talk to me