Please, what on earth does this sentence mean ? Does it mean I'm going to check out Europe, i.e. I'm going to investigate for my cultural education ?? (controlar = check, verify in PT portuguese).
No. "Controlâr" in PT Portuguese can, and often, means to check and/or verify. Control does not have that meaning in English. In English the synonyms you give are exact.
As a native portuguese speaker I can say that "controlar" usually means "to control", so the sentence should be read as "I am going to control Europe" as in conquering the continent. And actually it's not very common to use "controlar" as meaning "verify", and even when it is used the connotation is of control. When we want to say "verify" or "check" we use "verificar" and "checar".