Learn Farsi: شاید من آن رسید را قبل از مهلت فرستاده باشم. - I might have sent that receipt before the deadline.

Because the sentence starts with shâyad (maybe/might), the verb must express uncertainty. To talk about a past action that you might have done, Farsi uses the Present Perfect Subjunctive. It's built by taking the past participle ferestâdeh (sent) and adding the subjunctive form of the verb to be for I, which is bâsham.

Why is râ used after ân resid?

râ is the definite direct object marker. Because you are talking about that specific receipt (ân resid) rather than just any receipt, you need to use râ to show exactly what the target of the verb sent is.

I know ghabl means before, so why do we say ghabl az mohlat?

When linking before to a specific noun or event, Farsi uses the compound preposition ghabl az (literally: before from). Saying just ghabl mohlat is incorrect; you always need the az to connect before to the following noun.

Is the word man (I) strictly necessary here?

No, it is optional. The verb bâsham already clearly shows the I subject, so Farsi speakers often drop the man. Including it here just adds a little bit of emphasis, like saying I myself might have sent it.