"Мой брат ест рис и яблоки."

ест: eat есть: have/has

Yep. For neuter nouns (молоко, яблоко) and inanimate consonant-ending masculine nouns like рис (not like папа), as well as ALL inanimate plurals, the Accusative is the same as the Nominative. It is pretty convenient for a learner, right? Animate consonant-ending masculine nouns use the Genitive form instead (this behaviour also extends to all animate plurals).

The only type of nouns that has a unique form here is -а/-я ending nouns, most of which are feminine (ма́ма, земля́, хи́мия, матема́тика, страна́, Ита́лия) but some are masculine or common gender (па́па, дя́дя, пья́ница, судья́):

• Я ем рис, я́блоки и лук. (same as the Nominative)
• Я пью сок и молоко́. (same as the Nominative)
• Я ем ка́шу. (dictionary form: "ка́ша")
• Я пью во́ду. (dictionary form: "вода́")
• Тролль ест мою́ сестру́ (dictionary form: сестра́; note that animacy does not matter).
• Тролль ест моего́ бра́та (same as the Genitive).
• Тролль ест хлеб и пьёт пи́во (Nominative: these are сок/молоко-type nouns).
• Драко́н ест э́льфов, люде́й и гно́мов. (all plural and animate, all in the Genitive form)

Again, here is the rule which nouns have Accusative the same as Nominative:

• PLURAL: all inanimate nouns
• SINGULAR: neuter nouns, including ten nouns like и́мя/вре́мя
• SINGULAR: inanimate consonant-ending masculine nouns (сок, рис, контро́ль, хлеб). Having a consonant at the end is the most typical masculine patterb: Russian does not have THAT many nouns like папа and дядя.
• SINGULAR: ь-ending feminine nouns (мышь, ночь, крова́ть etc.)

Now, the nouns that have Accusative the same as Genitive:

• PLURAL: all animate nouns
• SINGULAR: animate consonant-ending masculine nouns (брат, отец, челове́к, учи́тель)

This only leaves feminine(and masculine) а/я-nouns not covered—and these have a unique У/Ю ending

It is supposed to be "Мой" with a "Й" in place of "Мои". "Мой" is used for masculine singular nouns, while "Мои" is used for plural nouns.