Learn Farsi: من هرگز مستقیماً با مدیرعامل صحبت نمی‌کنم.

This is the Arabic suffix ـاً (-an) that turns adjectives into adverbs of manner. Here, it attaches to the adjective مستقیم (direct) to create the adverb مستقیماً (directly). You will see this double-dash mark (called a tanvin) a lot on adverbs borrowed from Arabic!

Since هرگز means never, why is the verb صحبت نمی‌کنم also negative? Doesn't that make a double negative?

Yes, it does, and that is exactly how Farsi grammar works! Whenever you use negative adverbs or pronouns like هرگز (never) or هیچ‌وقت (never/at no time), the verb must also be negative. In Farsi, double negatives reinforce each other rather than canceling out.

How is the word for CEO, مدیرعامل, put together?

It is made of two words joined by an ezafe (the invisible 'e' sound linking nouns). مدیر means manager or director, and عامل means acting or agent. So مدیرعامل (pronounced modir-e amel) literally translates to managing director.

I noticed the preposition با (with) is used here. Can I use به (to) instead, like when saying 'speak to the CEO' in English?

In Farsi, the compound verb صحبت کردن (to speak/talk) almost always pairs with the preposition با (with). Even if you would say 'speak to' in English, you should stick to using با in Farsi to sound natural.