"You speak English and I speak Romanian."
Translation:Tu vorbești engleza și eu vorbesc româna.
The standard variants are "Tu vorbești limba engleză" and "Tu vorbești engleza". In everyday speech, you are likely to hear people say "Tu vorbești engleză", but that is not literary.
You can use the form "engleză", i.e. without the article, in a sentence such as "Tu vorbești în engleză". This has a different meaning though; the difference is explained here: https://english.stackexchange.com/questions/218506/speak-english-vs-speak-in-english.
Yes, but there are a few cases where including the pronoun adds clarity to the sentence. For example, "Vorbesc româna" could mean either "Eu vorbesc româna", "Ei vorbesc româna" or "Ele vorbesc româna".
About the Duolingo sentence "Tu vorbești engleza și eu vorbesc româna", here there is a contrast between you ("tu") and I ("eu"), so in this type of sentence the pronouns are included for emphasis and clarity.
It is a matter of choice. One can say „Vorbesc limba română.”, „Vorbesc româna.”, or even „Vorbesc românește.” (using an adverb). I would literally translate "I speak Romanian." as „Vorbesc română.”/„Vorbesc românește.”, and "I speak the Romanian language." as „Vorbesc limba română”. Hope this helps!
Can Duolingo please make up its mind on how the Romanian word for English is spelt. As you will see in the translation at the top of this discussion they have spelt it engleza. I was informed after doing this sentence that I ought to take care and put in the required accents and that I should have used engleză. However, I had not typed engleza. I used the word blanks and Duolingo has engleza on the word blank. So, Duolingo, please, if you want the spelling engleză ensure its on your word blanks.