Learn Farsi: او راننده است.

No, Farsi pronouns are completely gender-neutral! او can mean "he" or "she" depending on the context. In this sentence, we just happened to translate it as "she", but "He is a driver" is written exactly the same way: او راننده است.

Why is there no word for "a" before راننده?

In Farsi, you do not use indefinite articles (words like "a" or "an") when stating someone's profession. While in English we say "She is a driver," in Farsi you simply say "She driver is" (او راننده است).

The lesson teaches attached (enclitic) verbs, but است is written as a separate word here. Why?

While the copula endings -am (I am) and -i (you are) attach directly to the end of the previous word, the 3rd person singular form است (is) is an exception in written Farsi. It stands alone as a full, separate word.

Does the letter "heh" (ه) at the end of راننده make an "h" sound?

No, it makes an "eh" sound. At the end of many Farsi words, including راننده (rānandeh), the letter "heh" (ه) acts as a vowel rather than a hard "h" consonant.