What is the difference between "a" and "az"?
A alma = the apple
Is it a genre difference?
"Az" goes before words starting with a vowel, "a" goes before words that start with a consonant. It's like "a" and "an" in English.
You saw "A alma in the course?" That's wrong - even I know that. :) Might've been a typo.
why wouldn't "a kocsi" count as a right answer?
It could. If you report it, maybe they will add it to the accepted translations.
kocsi- is wrong