"We talk to each other often."
Translation:Nous nous parlons souvent.
I put "on nous parle souvent", and was marked wrong. It suggested "on se parle souvent". I agree that "on se" would be correct, and obviously "nous nous" would too, but I'm not sure that "on nous" would not.
Is it? Even in the case (like this) where the "se" or "nous" or whatever is not really "part of" the verb? I'm not sure how exactly to phrase that, but I mean: It seems like there's a difference between verbs like "to give", where both "je me donne" and "je te donne" would make sense, and verbs like "remember", where "je me souviens" makes sense but "je te souviens" (as far as I know) does not.
Also, I'm pretty sure Duolingo has previously marked me correct in similar (but not the same) cases, like "on aime bien notre professeur" rather than "on aime bien son professeur".
Finally, googling on French Google for "on nous parle" gives a whole bunch of hits, but I'm not fluent and I don't know if they mean "we talk to each other" or not.
Your confusion comes from the on=nous equivalency. This is one that is true, in spoken French, and is becoming more and more prevalent (to the point that using "nous" in a casual conversation might sometimes sound a bit pedantic - i may be overstressing the point but that's where the language is heading).
I tried to explain (see below), but it is turning into a wall of text and I realise i won't necessarily be able to give steadfast rules. So maybe pull https://www.thoughtco.com/the-many-meanings-of-the-french-subject-pronoun-on-3572148 instead
The thing is "on" also keeps its other meaning of "impersonal pronoun", as is probably best linked to the English "one". One shouldn't eat with their mouth full = on ne mange pas la bouche pleine. That "on" is not at all "we". It is either some indefinite person that serves as an ideal to reach (like in the mouth full example), or as a way to target a person or group without naming them: "On ment aux Français" = "the French are being lied to". By whom? It is not said, either because it is unknown or simply to avoid the trouble that could be cause by accusing someone.
In your sentence, you mix both sides of the coin. This, sadly, is permitted in some legit sentences because the "on" as synonym for "nous" does not have a full set of cases like other pronouns (eg "je" has "me", "mon/ma", etc.) and instead borrows either the first person plural ones or the third person singular (which is the default for "on" as impersonal pronoun).
The clean: - On aime son voisin = One loves (or ought to love) their neighbor - On aime notre voisin = We love our neighbor (That's pretty much your "professor" example. Also note that the first of these two could just as well mean "We love his/her neighbor", so maybe it isn't that clean after all)
The muddy: - Nous nous parlons = we talk to each other (or one another) - On se parle = we talk to each other (or one another)
- On nous parle = someone talks to us, we are being talked to
All in all, this is a relatively recent evolution of the language (the "on" as "nous") and is therefore quite unsurprisingly causing a big mess that finds case-by-case resolutions and probably won't show any sort of consistency for another several decades.
Another comment for your thoughts on reflexive verbs (the ones that have "se" as a part of their infinitive), hopefully later today.