"He is not vegetarian."
Translation:Αυτός δεν είναι χορτοφάγος.
So I have trouble memorizing the word vegetarian and thought I could associate χορτο with "horti" in horticulture to help me remember. But it turns out that the prefix is indeed Latin (hortus - garden), instead of Greek. Etymology is so hard! Am I wrong and the two words are just coincidentally close in sound / appearance?
See this discussion: https://www.duolingo.com/comment/17556409. I can't quite make out what transliteration rules have been followed in this course, but it seems very likely that there are more than one spelling mismatches in your answer - if transliteration for this sentence is available.
May I ask, why don't you use a Greek keyboard? You'll never see Greek written in the Latin alphabet outside texts from friends or in online comments and even then, everyone follows different spelling rules according to their own visual preferences (and knowledge of orthography ;).
Is χορτοφάγος always masculine or is there a feminine and neuter form?
Classically, adjectives that are compound words (as χορτοφάγος from χόρτον + φάγειν) have one common ending -ος for masculine and feminine forms, and a separate one -ο (formerly -ον) for neuter.
So it would be ο χορτοφάγος άντρας "the vegetarian man", η χορτοφάγος γυναίκα "the vegetarian woman", το χορτοφάγο παιδί "the vegetarian child".
According to Wiktionary and my trusty paper dictionary, though, this is one of many adjectives that has been partially modernised and can have a separate feminine form: η χορτοφάγη γυναίκα (though Greek Wiktionary says the separate feminine form would be η χορτοφάγα γυναίκα).
As a noun, though, the masculine and feminine forms are the same: ο χορτοφάγος "the vegetarian", η χορτοφάγος "the (female) vegetarian".
In this, it acts like many other nouns in -ος referring to people (mostly professions) which can be masculine or feminine, e.g. ο/η γιατρός "the doctor".
Is it possible to use είναι δεν χορτοφάγος?
Does the δεν particle always go before the verb?
Yes, though not necessarily directly before it -- short-form object pronouns are closer to the verb for example: Δεν σ' αγαπώ "I don't love you"; Δεν μου αρέσει "I don't like it".