Learn Dutch: Wij zitten te studeren voor het pittige tentamen.

Using a posture verb like zitten (to sit) plus te and an infinitive is a common Dutch way to express that an action is currently ongoing. It is similar to the English continuous form (are studying). Because you typically sit down to study, zitten is the natural choice here to emphasize that you are busy doing it right now.

I thought pittig meant spicy food. Why is it used to describe a test here?

While pittig does mean spicy when talking about food, it is very commonly used in a figurative sense to mean tough, challenging, or intense. Therefore, het pittige tentamen translates to the tough exam.

Tentamen is a het word. As a quick refresher, why does the adjective pittige still get an extra -e at the end?

Adjectives placed in front of a noun almost always get an -e ending. The main exception for a het word is when it is preceded by an indefinite article like een (a) or by no article at all. Since this sentence uses the definite article het, the adjective pittige keeps the -e ending.

Is there a difference between a tentamen and an examen?

Yes, they are used in different contexts. An examen usually refers to a major final exam, such as high school finals or a driving test. A tentamen is a specific term used in Dutch higher education (colleges and universities) for a standard exam taken at the end of a specific course or semester course.