Learn Farsi: این مسافر خودش را نجات می‌دهد.

To say "himself" (or "herself"), we take the base word for "self", which is khod, and attach the third-person singular possessive ending -ash. Then, because "himself" is the specific direct object receiving the action of the verb (the person being rescued), we have to add the direct object marker râ.

I learned that mi-dahad means "he/she gives". Why does this sentence translate to "rescues"?

"To rescue" or "to save" is a compound verb in Farsi: nejât dâdan (literally "to give rescue"). When forming the present tense, the noun part (nejât) stays the same, and the verb part (dâdan) conjugates to match the subject. Here, it becomes mi-dahad to match "this passenger".

Would the word khodash change if we knew the passenger was a woman?

No, Farsi does not have grammatical gender. The ending -ash can mean "his", "her", or "its". Therefore, khodash translates to "himself", "herself", or "itself" depending entirely on who the subject is.

In everyday spoken Farsi, how is khodash râ usually pronounced?

In conversational Farsi, the direct object marker râ usually merges with the noun or pronoun before it. Khodash râ commonly blends together and is pronounced as khodesho.