Sorry but in French "carte" does not mean "letter" at all. Letter in French is lettre (actually English took the word from French). "Carte" in French means "card" or "map", depending on the context. I guess you are confused because of the Spanish "carta", which does mean "letter".
"Ea" in "cartea" is a diphthong, so the two vowels are pronounced together. Here you can get an idea what this group is supposed to sound like: https://www.romanianlesson.com/romanian-vowels-pronunciation-together
And while I'm at it, what is the infinitive of "to drink"? Plus, I noticed that the "accents" on the verb "to eat" change (as if it wasn't difficult enough to pronounce, they also have to change!! ;) ). Or did Duo make a mistake? I somehow don't see it logical that they would change. Could you maybe write down the infinitive of "to eat" and all the six forms in the present tense?
Thomas, 'a mânca' is an irregular verb. Luckily, there aren't many of them in Românian. And btw Ă, Â are not accents on A but individual letters on the alphabet. And at least Â/Î stands for a very distinct sound, similar to that in Bulgarian or Turkish (Ъ and dotless I, respectively).
a citi = to read
Eu citesc = I read/I am reading
Tu citești = You read/You are reading
El/Ea citește = He/She reads//He/She is reading
Noi citim = We read/We are reading
Voi citiți = You read/You are reading
Ei/Ele citesc = They read/They are reading (ei - is for masculine plural, ele - is for feminine plural)
a scrie = to write
Eu scriu = I write/I am writing
Tu scrii = You write/You are writing
El/Ea scrie = He/She writes//He/She is writing
Noi scriem = We write/We are writing
Voi scrieți = You write/You are writing
Ei/Ele scriu = They write/They are writing
Ea citește o carte = She is reading a book/She reads a book
Ea scrie o carte = She is writing a book/She writes a book