Learn Farsi: دیروز باهاش حرف زدم.

باهاش is the spoken, colloquial way to say "with him", "with her", or "with it". In formal written Farsi, you would use با او for a person. In everyday conversations, native speakers almost always contract the preposition با (with) and the pronoun into باهاش.

The translation says "with him", but could this sentence also mean "with her"?

Yes! Farsi pronouns are entirely gender-neutral. The colloquial word باهاش can mean "with him", "with her", or "with it". You would know which one it is based on who was being talked about earlier in the conversation.

Why is the verb زدم used here if that word usually means "I hit"?

In Farsi, "to talk" or "to speak" is the compound verb حرف زدن. It literally translates to "to hit speech" or "to strike words". Here, حرف زدم is simply the simple past tense form, meaning "I talked".

Why is there no Farsi word for "I" at the beginning of the sentence?

The pronoun من (I) is dropped here, which is very common in natural Farsi. The verb ending ـم in زدم already makes it perfectly clear that "I" am the person who did the talking, making the extra subject pronoun unnecessary.