Learn Farsi: همه‌ی ما با هم شام خوردیم.

While har means "every" and is followed directly by a singular noun (like har ruz for "every day"), hame means "all". To say "all of us", we use hame plus the pronoun ma (us). When linking hame to a pronoun or noun, you must use an ezāfe connection, which you don't do with har.

Where does the "of" in "all of us" come from in hame-ye ma?

It comes from the ezāfe, the grammatical "glue" that links words together in Farsi. Because hame ends in a vowel, the ezāfe takes the form of a "ye" sound. So, hame-ye ma acts like "the all of us".

Does ba ham literally translate to "together"?

Literally, ba means "with" and ham means "each other" (or sometimes "also"). So ba ham translates to "with each other", which is the most natural way to say "together" in Farsi.

The English translation says we "had dinner", but doesn't khordim mean "we ate"?

Yes! In English, it is common to say we "have" a meal, but in Farsi, you always "eat" (khordan) meals. Therefore, "we had dinner" is translated as "we ate dinner" (sham khordim).