Actually I would use both. I would write it ON my calender if it was a calender hanging on the wall. I would write it IN my calender if it was a little pocket calender or the one on my phone.
"I write it on my calendar." is also accepted by Duolingo. At least it is now if it wasn't before.
Apparently nothing, though to me it feels wrong. To me a calendar is a thing you hang on the wall, a surface, that you write on. Not a book-like thing like an agenda, that you write in. But that's my faulty brain, alright:p
Yeah, I think that's our Dutch interpretation. As far as I know, the word "calendar" can be used for both our "kalender" and "agenda" in English.