Learn Farsi: من درباره‌ی جرم صحبت نمی‌کردم.

The compound verb here is صحبت کردن (to talk). To make it negative past continuous, we leave the non-verb part صحبت alone and modify the verb part. We combine the negative prefix ne-, the continuous prefix mi-, the past stem kard, and the personal ending -am for 'I'.

Why is the negative prefix pronounced ne- instead of na-?

Usually, the negative prefix is na-. However, whenever it attaches directly before the continuous prefix mi-, its pronunciation always shifts to ne- to make it easier to say. That is why it is ne-mi-kard-am and not 'na-mi-kard-am'.

Why does the word درباره (about) have a ی attached to it here?

The word درباره ends in a silent 'h' which acts as a vowel. Because it is linking to the next noun جرم (crime), it needs the connecting grammatical vowel called the ezāfe. To link two vowels smoothly, Farsi adds the consonant ی (y), making the ending sound like '-ye'.

Could we drop the pronoun من from this sentence?

Yes, absolutely! Because the verb ending -am in نمی‌کردم already clearly means 'I', the word من is completely optional. Using it here just adds a little extra emphasis to the fact that it was you who was not talking about it.