Learn French: Mon cousin a souvent bâillé malgré le café. - My cousin often yawned despite the coffee.

In French compound tenses like the passé composé, short and very common adverbs (such as souvent, bien, déjà, and beaucoup) are usually placed between the auxiliary verb (here, a) and the past participle (here, bâillé).

Since souvent means 'often', doesn't that make this a habit? Why aren't we using the imparfait tense?

That is a great catch! While souvent can describe a past habit used with the imparfait, here the passé composé is used to describe a specific, completed timeframe (like during a single meeting or movie). He yawned several times during that specific event, rather than it being a general ongoing habit from his childhood.

English speakers say 'in spite of'. Do I ever need to add de and say malgré de le café?

No, malgré simply means 'despite' or 'in spite of' all by itself. It is directly followed by a noun and its article. You will never use de right after malgré.

If the subject was a female cousin (ma cousine), would bâillé need an extra 'e' at the end to match her gender?

No, it would stay exactly the same: ma cousine a souvent bâillé. Because the auxiliary verb is avoir (a), the past participle does not agree with the subject's gender or number. It would only change if a direct object came before the verb, which isn't the case here.