Why is le carte marked incorrect?
Because carte is feminine, so you can't use the singular masculine definite article with it.
Again, it marked me wrong for not knowing a word it hasn't actually taught me yet ("plan")
My three choice for "The map" were
1 La fenêtre
2 La livre
3 Le plan
I picked le plan thinking it might be right because you plan out a route. But is this a real option or just a mistake by duolingo?
"Le plan" is the masculine version of the English "map", so it is indeed correct.