Learn Farsi: اول غذا می‌خوریم، بعد می‌رویم.

بعد از (ba'd az) is a preposition meaning 'after', which must be followed by a noun or pronoun (like 'after dinner'). When بعد (ba'd) is used all by itself without از (az), it acts as an adverb meaning 'then' or 'afterwards', which fits perfectly here.

The translation says 'First we eat', but doesn't غذا (ghazaa) mean 'food'?

Yes! While you can theoretically just say می‌خوریم (we eat), Farsi speakers usually say غذا می‌خوریم (literally 'we eat food') when referring to having a meal. It sounds much more natural and complete.

These actions haven't happened yet, so why are we using the present tense verbs می‌خوریم and می‌رویم?

In Farsi, the present tense (marked by the می prefix) is frequently used to talk about the immediate or planned future. This is very similar to English, where we casually say 'First we eat, then we go' instead of 'First we will eat...'.

Why aren't we using the pronoun ما (we) at the beginning of the sentence?

Because the verb endings (-یم in both verbs) already tell us that 'we' are the ones eating and going. Farsi subject pronouns like ما are often dropped in everyday speech unless you want to emphasize who is doing the action.