Αδερφός and αδελφός is the same word . Actually in greek language αδερφος is more common .
Yes, and either is accepted throughout the course. If it is not; let us know so we can correct it.
The ancient word is αδελφός but it's not surprising that αδερφός is a common alternative since the "liquid" letters (lambda and rho) have always been interchanged in Gk historically. There is, for instance, abundant evidence for phonetic exchange of λ και ρ in the Gk papyri (see Francis Gignac, A Grammar of the Greek Papyri of the Roman and Byzantine Periods  volume 1, p. 105). Highly recommended is G. Horrocks, Greek: A History of the Language and its Speakers (2nd edition; Blackwell, 2014) for interesting phonetic changes in Gk historically, homophonous letters, Atticism, and the rise of Katharevousa.
''My brother's a student." is indeed a correct translation and is included in the incubator.
Hi. I'm a little bit confused. μαθητής must be pronounced as 'mathitis', or am I wrong? In the audio says 'mathetes'. In others exercises when η is accentuated sounds like the first 'e' in 'element', but when it's not, it sounds like 'ι'. :S
One of the best features of Greek is that letters are always pronounced the same (with very few exceptions). So, "η" is "ee" as in "see". If it sounds different on an audio exercise it's because they are created by a computer TTS. So, it is "ee" in every part of the sentence. Here is a link where you can hear native Greek speakers:
"One of the best features of Greek is that letters are always pronounced the same (with very few exceptions)."
I absolutely love this feature of the Greek language. It's a lot like Spanish and Italian in that sense. ( ͡ᵔ ͜ʖ ͡ᵔ )
How can we distinguish from "my brother is student" because there is no 'ενας' here.
I understand your observation. I can only speak for the romance languages (Spanish, French, Italian, etc.), which tend to omit the indefinite article (a, an) in many of their sentence constructions, much like Greek. In English, however, we have no choice but to write the indefinite article so that the sentence is grammatically correct.