Learn Dutch: Het zweet stroomt over mijn gezicht. - The sweat is pouring down my face.

You can turn this into an emphatic exclamation by starting with of and using subclause word order, moving the verb to the end: Of het zweet over mijn gezicht stroomt! This structure is used by native speakers to strongly affirm that something is happening, translating roughly to 'And HOW the sweat is pouring down my face!'

Why does the Dutch sentence use over instead of a word for 'down' to match the English 'down my face'?

In Dutch, fluids moving across a surface generally use the preposition over. While English focuses on the downward direction of the movement, Dutch focuses on the area being covered (over mijn gezicht).

The English translation says 'is pouring', so why didn't we use a continuous form like is aan het stromen?

While you can technically use the aan het continuous form in Dutch, it is required much less frequently than the English '-ing' form. For an ongoing natural process like sweat flowing, the simple present (stroomt) is completely natural and almost always preferred.

Could I use the verb gieten instead of stromen since the English translation is 'pouring'?

Not for sweat. Gieten is typically used for actively pouring a liquid from a container (like tea) or for very heavy rain. For bodily fluids naturally moving across the skin, like sweat or tears, stromen (to flow or stream) is the correct verb.