In Greek the indefinite article can be omitted very often. Η καμήλα είναι ζώο and Η καμήλα είναι ένα ζώο are both correct :)
In English a animal is incorrect. When a word starts with a vowel (a,e,i,o,u) the word is preceded by the word an. An animal, an elephant, an insect,....) I was told I had a typo error.
There's actually a constellation called Camelopardalis, coming from Latin and Greek, meaning giraffe. The idea according to a couple of dictionaries is that the giraffe was thought to have the head of a camel and the spots of a (leo)pard.
They are different forms of the same verb -- you have to pick the one that matches the subject.
A bit like how you can't say "he am" or "you is" or "I are" in English: those are all forms of the verb "to be" but they're not the right one for that subject.
είμαι is the form for εγώ: εγώ είμαι "I am"
είναι is the form for αυτός, αυτή, αυτό, αυτοί, αυτές, αυτά (he, she, it, they), e.g. αυτός είναι "he is" or αυτές είναι "they are".