Others might be able to help you better if you were a little more specific about what's confusing. :)
Is there any difference between "Corinna femina est" and "Corinna est femina"?
As J.C.M.H. said, word order in Latin is free (with some exceptions), but SOV is the most common. Changing the order would change the emphasis (like "Corinna is a woman.") but no more than that.
No; word order in Latin is rather free; only the sintax Corinna femina est would have been more common in Classic Latin. For instance, the famous phrase Alea jacta est "The die ist cast".
Latin in Duolingo! It's wonderful! I would not have imagined it. Thanks, Duo.
As far as I remember from my lessons more than 40 years ago, wouldn't it rather be: Corinna mulier est. I think mulier is more commonly used for woman than femina.
Mulier is also accepted, but the course teaches femina first because it's more faniliar to English speakers.
Because sum is the first person singular; here we need the third person singular, est, because of Corinna.
S O V is the most common, standard word order in Latin, with the verb at the end. Other orders are also possible and accepted, though.
Yes. Because just like any other noun and pronoun, names get declined and you need to learn the different forms. And when writing in English, they said to not translate but to keep the nominative form.