Мой друг кивает и улыбается.

the friend

Breakdown of Мой друг кивает и улыбается.

• мой: my
• и: and
• улыбаться: to smile

Questions & Answers about Мой друг кивает и улыбается.

Why is it мой, not моя, моё, or мои?

Because друг is a masculine singular noun, and мой has to agree with it.

• мой = masculine singular
• моя = feminine singular
• моё = neuter singular
• мои = plural

So:

• мой друг = my friend (male friend, one person)

What case is мой друг in?

It is in the nominative case, because it is the subject of the sentence — the person doing the actions.

Here, друг is the one who nods and smiles, so nominative is the expected case.

Why do the verbs end in -ет and -ется?

Because the subject is third person singular: мой друг = he / my friend.

So the verbs are in the present tense, 3rd person singular:

• кивать → кивает
• улыбаться → улыбается

Russian does not need a separate word like English is here. The verb form itself already tells you the tense and person.