Saru actually passed the Kobayashi Maru. Mind you he wasn’t the one taking the test. A pyrotechnic went off early in the simulator and knocked out the cadet going through the program. Saru had to take over as acting captain and managed to save everyone.
The Universal Translator is basically magic. TOS came closest to describing how it works, and it boiled down to, “IDK man it does some brain scans to detect your language structure”. There’s no satisfying answer as to why it knows the “Washington State Bridge” is a combination of a proper noun, a geopolitical concept, and a general noun.
In Enterprise, the Universal Translator is generally depicted as a modern miracle of technology, but one without useful internal intelligence. If it hears a few snippets of Romanian, it’s just going to start brute forcing a translation matrix with every technique it has at its disposal. More speech gives it more data to work with, but it’s still just cycling through its options.
Sato’s familiarity with xenolinguistics allows her to aid the Universal Translator by narrowing the system’s options or directing it down specific paths. She doesn’t know or learn the alien languages in the traditional sense, but she’s shown for having a knack for picking up on patterns and syntax. Again with the Romanian example, she’s doing the alien equivalent of saying, “This sounds European, skip trying to translate this as an Asian language for now”. The Universal Translator has fewer options to run through and gets to a successful translation matrix faster.
But again, it’s plot contrivance space magic.