Translation:We thought Saint Petersburg was a city in Germany.
Not an expert so I might be wrong on this, but as a native French speaker, the suffix "bourg" does not necessarily evoke latin origins to me. Wiktionary says -bourg comes from latin burgus, which itself comes from old germanic burg Even though Strasbourg is today in France, I don't need to mention the painful history of the region and I'm pretty sure the name of the city is actually of Germanic origin (Wikipedia confirms it). There are cities with -bourg or bourg- in France and I guess in those cases the origin can be latin, but do not assume that this the case all over Europe, the origin could very well be germanic (think Luxembourg). In the case of Saint Petersburg, Wikipedia says it was inspired by the Dutch suffix -burg, so most likely germanic in this case
You can drop «что» in such sentences. But of course, if you use it, it’s OK too.
I think it depends on the verb. With some verbs «что» can be easily dropped (like думать 'think', полагать 'to believe', слышать 'to hear', видеть 'to see' when it is used metaphorically), while with others it sounds colloquial and informal (видеть 'to see' when it refers to actually seeing something with your eyes, знать 'to know').