That comment... That profile picture...
You deserve extra lingots for this alone XD
I believe сок is masculine singular so you use the "my" that matches masculine singular, which is мой
"моя" is nominative feminine singular form of "my" - e.g., "моя собака" = "my dog"
"мой" = nominative masculine singular form of "my" - e.g., "мой сок"
It is not like «меня сок» means anything in particular: it is just "me" and "juice" put side to side.
There's this piece of translation in Tips and notes: яблоко мамы = mom's apple. I guess, then: would "сок меня" be correct?
It wouldn't. The Genitive меня, тебя, себя, вас, нас are not used as possessives, just like you cannot use "me dog" or "us fish" in English—"my", and "our" are used instead. With 3rd person pronouns, however, the possessives indeed derive from the pronouns' Genitive forms, so they look like его, её and их.
No. "Моего сока" would be the genitive form of "мой сок", so it could make sense. But both words have to be in genitive.
I think that this is the 8th exercise I done in this module involving "my juice" or "мой сок". I actually understood it pretty well 6 exercises ago. Would be nice to see how it works with "your/his/her/our/their juice" instead.