This is marked as spoken language. It is quite common. I would also argue that it's informal.
Even if you take /pour/ to mean /au sujet de/, which it does here, there is something "left out". Putting in /au sujet de/ here for /J'ai appris au sujet de ton père/ is not even grammatical. And the /pour/ used like this is grammatical only in speech. And, /j'ai appris pour ton père/ is only grammatical in speech.
You would not see in a formal text: /L'institution a été informer pour les livres/. To mean: /L'institution a été informé que les livres seront livré par coursier/. In this example, /pour/ stands in for the entire idea of the books being delivered by messenger.
But, you might hear someone say that.
pour + noun or pronoun can stand for any number of contexts or co-texts that are not in the actual utterance.
In /Le médecin m'a dit pour les examens/, therefore one has to know what the context is. Here, it's not: The doctor told me about the tests or exams. It's something like: /The doctor told me that tests were being done or needed to be done or were done/.
Only a wider context will make it clear exactly.
With apprendre, here, for instance, it's /J'ai appris que votre père est mort ou est décédé [or apprendre la mort de ton]/ or something like that. Using the pour becomes a way to avoid having to say: /I was informed or learned of the death of your father/.
Contextually, the /pour/ + /noun or pronouns/ can replace an entire context or idea.
In English, /J'ai appris pour votre père/ would be: /About your father, I heard/. Or /I heard about your father/. The funny thing here is that in English, /I heard about your father/ is completely standard both in speech and in writing, and the spoken French aspect is lost since there's not really any way to render it in the marked sense of spoken language.
[Kindly do not remove the slashes. I have re-edited myself for how I want the text to read. Thank you for your cooperation.]