For anyone confused,
In the nominative case (discussing sentence subjects), you use мой (moy) for masculine nouns (that is, nouns that end with a consonant, й, or some words that end in ь)
You use моя (moya) for feminine nouns (that is, nouns that end with а, я, or the other words that end in ь)
You use моё (moyo) for neuter nouns (that is, nouns that end in о or е)
Lastly, you use мои (moi) for plurals.
There are a few exceptions, of course. For example, you say мой папа (moy papa) (my dad), мой кафе (moy kafe) (my coffee), мой дядя (moy dyadeh) (my uncle), мой дедушка (moy dyedushka) (my grandpa), and мой мужчина (moy mushchina)(my man, more like my husband). These are probably the only ones you'll run into in casual conversation.
Just minor correction.
cafe = кафе
coffee = кофе
моё кафе (neuter)
мой кофе (masculine)
As for кофе it is very typical error for many russians to say "моё кофе" as language feeling makes it think about this word as a neuter noun. It was even added to some orfographic dictionaries as neuter and there was wide discussion about it. People who know the correct gender of this word are very proud of their knowledge.
What are the different forms of "my" in russian and when do you use each one?
There are four different "forms" of "my" in the nominative case(one of six Russian cases, it is used to on verbs which act as the sentences subject). Which one you use depends on the gender/number of the object "my" possesses. For masculine nouns you use Мой, for feminine nouns you use Моя, for neuter nouns you use Моё and for plural nouns you use Мои. I hope this helps. :)
For the curious there's a full table here, under "Declension":
From the link that you provided nom. neuter my = мае́
From Duo and comments on this page nom. neuter my = Моё
I can see that studying a non latin language is going to introduce transliteration problems where I hadn't expected them.
There are lots of transliteration systems out there but you would be 100% correct to just write мое as moe and call it good, since many translit systems don't differentiate between ё and е (I can't talk for the system they use on Duolingo specifically though).
Молоко is my favourite Russian word! There is the band Moloko and they drink "moloko plus" in A Clockwork Orange!
And "хорошо" must have inspired the adjective "horrorshow" in that movie!
моё молоко - milk has no accent, but, it did in an earlier lesson: Молоко́. There was no mention of accents disappearing in the "Basics 2 - Lessons: Tips and notes", but, it happens to milk in "my milk", and to water, вода́, in "my water", моя вода ? Would someone please explain it to me? Thanks!
Those aren't accents but educational stress indicators to help you learn the pronunciation of the word.
I have had both "мои молоко" and "моё молоко". Both time i got it correct "my milk" can anyone explain the difference or why they are both ok to use?
Well, one actually wrong so I don't know why the course accepts that (probably just an accident). Мои is my, but you use it with plural nouns. Моё is also my, but you use it with singular neuter nouns.
ё is io (I think of it as yo), е is 'ye', and э is 'e', as in 'end'. I agree е does often sound like just 'e', but actually it is pronounced 'ye', as in её (yeyo), or нет (nyet).
There is a very good table here: http://www.russianforeveryone.com/RufeA/Lessons/Introduction/Alphabet/Alphabet.htm