Translation:A student is waiting for somebody near the library.
"To wait on (someone)" in the sense of "to wait for (someone)" is a variant that has become more common in recent years, at least in North American English. But to my ears, this "to wait on" (= "to wait for") sounds like a regionalism (perhaps originating in the Southern states?) and is certainly substandard. "To wait on," as Neon_Iceberg says, really means "to serve as a waiter." No educated person would say "Waiting on Godot" … I offer this as a native speaker of North American English.
In its most common usage, “to wait on” means to serve like a waiter. But it can also do double duty and be used in a sense similar to “wait for.” There are cases when a student can wait on someone/somebody, so I think your choice is should be accepted, but the Russian one is closer to "waiting for".