hm so I'll leave my native romanian opinion here, pretty much enforcing what you say. Pardon is used for casual situations like when you accidentally bump into someone and when it's your fault. However, desole, is better for worse cases, when you mess up badly, but also for bad things happening: eg someone says they're bike was stolen, you can say desole, but not pardon
"Je suis désolé" or "Je suis désolée" are both ok. The voice is only a computer.
As Duo is only a computer and don't what is your gender, it accepts male and female adjectives as long the sentence is grammatically correct. Except if you have a clue in the sentence to show you have to use the male or the female form (and it's not the case here)
For instance: "Elle est désolée", can be only the female form.
I wrote "I am upset" and Duolingo tells me it's not correct. But it was Duolingo who told me that désolé could be sorry or upset. I prefer upset so I can differentiate it from "pardon".
As Duolingo may be wrong, could someone tell me if "I am upset" is OK for désolé? Thanks a lot
"désolé" has several meaning. When you use it in the expression "Je suis désolé", it always means "I'm sorry". The other uses of the word "désolé" is litterary, and it means "lonely" in the expression "un paysage désolé", (lonely, sad, abandoned, desolated), the English "desolated" is from the French "désolé".
The third meaning is to saden, to make very sad. Cela me désole = it makes me very sad.
But these two meanings are very far from "sorry", don't confuse them!
Distressed or upset = bouleversé, not "désolé".
"bouleversé" and "désolé" have a very different meaning. Bouleversé here: http://dictionnaire.reverso.net/francais-anglais/boulevers%C3%A9