I see furtively used more in fiction writing. To sound like an American (and you know how weird we can be), I'd say, "Have you been sneaking pictures of me?" To be a little more proper (but still natural), "Have you been taking pictures of me without my permission?" These are polite. As you might imagine, an angry man might say a completely different thing.

You could ask: Have you secretly photographed me? Have you secretly taken pictures of me? or Have you taken pictures of me without my permission/knowledge?

My feeling is that outside of very formal professional speech, neither is natural. "Furtive" is not a word you will hear in everyday speech. I think you might hear the same thing described as "secretly", e.g. "Did you secretly take pictures of me?" "Have you secretly been taking pictures of me?" More likely, I'd say, is that you'd use the word "spying", e.g. "Were you spying on me?" "Have you been spying on me?"

I would say that many native speakers have never heard and certainly never used the word "furtive," and sneaky or even surreptitious for this kind of thing would be more common. But, in police jargon (and I was one) furtive (sneaky) glances is used all the time to show probable cause to stop, search, and maybe arrest. I love that word! Have fun with it.

No. The second sentence is correct. The adverb furtively is used to modify an action (for example: taken, hidden, or written). When used with got it sounds unnatural because got implies ownership without action. On the other hand, "Have you furtively gotten photographs of me?" does sound natural, because gotten refers to the action of obtaining the photographs.