Learn Dutch: De spion moet een zware proef ondergaan. - The spy must undergo a tough test.

It is inseparable here. When ondergaan means to undergo or to endure, the stress falls on the verb part (ondergaan) and it cannot be split. If you stress the prefix instead (ondergaan), it becomes a separable verb with a completely different meaning: to go down (like the sun) or to perish.

How would I write this sentence in the present perfect tense (The spy has undergone...)?

You would say: De spion heeft een zware proef ondergaan. Because this specific meaning of ondergaan is inseparable, its past participle does not get the extra -ge- prefix in the middle. If you were using the separable version meaning to go down, the past participle would be split by the prefix: ondergegaan.

Why use zware (heavy) instead of moeilijke (difficult) to mean tough?

In Dutch, zwaar is widely used metaphorically for things that are physically or emotionally draining, such as a grueling trial, a tough time, or a severe injury. Moeilijk is usually reserved for things that are mentally complicated or hard to figure out, like a puzzle or a math problem.

Does proef just mean a regular school test?

Usually not. For a standard school test, you would use toets, examen, or test. A proef leans much more towards a trial, an ordeal, or a scientific experiment. In this spy's case, een zware proef is best understood as a severe ordeal or a test of endurance.