On principle I have never (ever) used hovering hints in german. Or italian or french. Too much of a crutch, l've thought. But in slavic languages I do use them, I must say. I extensively use online and offline dictionaries, with shortcuts on the desktop, for all languages. Opening in a different browser for no ads.

Мой, моя, моё, are first person, possessive, singular pronouns in the nominative (but not necessarily exclusively the nominative) case, corresponding to masculine, feminine, and neuter genders respectively. Я, мне, меня, are first person, singular pronouns, corresponding, but not limited, to the nominative, prepositional, and genitive cases respectively.

When to use them is best answered with tables, so here they are:

Pronoun tables - http://www.russianlessons.net/grammar/pronouns.php

A table of the cases and their uses - http://www.alphadictionary.com/rusgrammar/casefunc.html

O/c, the gender of the noun determines the gender of the possessive pronoun to which it belongs.

Neuter, like most words ending with о

U use them depending on gender of noun. Moë for neuter moя for female мой for male мои for plural of either gender These mostly apply to the nominative case only