level of formality does not depend on the age difference but could be a part of it.
This is how you say I love you to a person you address as "pani" , not their name or Mother , Grandmother, Aunt, etc. (you can be formal to your mother - kocham Mamę).
So it's how you would say it your elder neighbour, or a teacher, or a celebrity you don't know. You can see and hear it in old movies/ books between two young people in times when using "ty" to address somebody was more restricted.
It is complicated. A bit of both. In formal situations you use Pan /Pani .
But it is also about respect and a bit about generation difference. My best friends Mom- I use Pani sitting on the floor in her living room and playing with her grandson.
The best example, and I think most common to happen is "kocham Panią" said by a child to its teacher.
It does sound strange in a teacher-student context, but I wouldn't say that it doesn't make sense in general. I could very well imagine hearing this in movies which are set in the 19th century, for example. But I agree, such usage would be very rare nowadays.
We all know that children don't always use the most apporiate words to describe their thoughts and feelings, as their vocabulary is still limited. So I don't see a reason why immery's example would be considered impossible.
So I am admittedly new to Polish, but when I am dealing with the formal you in other languages (e.g. French or Spanish) I liken it to whether I would address the listener with a Mister or Ms (or Miss/Missus, if that is her preference). This seems consistent with what the more experienced speakers are saying. For example, I called my teachers Mister and Ms. but I would never call my grandparents or parents that. It's probably not a perfect rule, but it seems to be the closest thing we have in English.
Not in all its usages. We used to differentiate between Panna and Pani when addressing women (like Miss and Mrs), now we don't. But it still means an unmarried woman (unlike English 'spinster' - stara panna - it doesn't have any negative connotations). Sometimes it can also refer to any young woman, or - coloquially - to one's girlfriend. And Panna is one of the zodiac signs - Virgo :)
In English, "equals" sometimes use "sir" and "m'am" in a gallant way--e.g., if they are bantering with each other, or exchanging pleasantries in an ironic way. E.g. I meet a friend at a restaurant, and say "good evening, sir! You're looking sharp today!" Or a man might greet a woman by kissing her hand and saying "you look lovely tonight!" Again, in a slightly ironic or archaic way.
Is the formal you used in Polish in this sense?
- Or a man might greet a woman by kissing her hand and saying "you look lovely tonight!" * it is archaic?
I think this sentence "kocham panią" could fit in larger "banter", but some archaic or more formal words would be used.
Pani/Pan is just polite way you talk to almost everybody.
It's singular accusative.
Why is that so? That's a good question. Other female nouns with the nominative ending -ni do in fact inflect differently (gospodyni -> gospodynię).
Pani can be both a noun and a pronoun. If we take a closer look at Polish pronouns, we can see that many of them lost the ę/ą-distinction a few centuries ago. Notable examples include moją, swoją, waszą, tamtą... That's the closest to an explanation I can come up with.