"Who is standing in front of the store?"
Translation:Ki áll az üzlet előtt?
No, that wouldn't be grammatically correct.
The only other possibility would be "az üzlet előtt ki áll?", but that puts the focus on the place and means something more like "and in front of the store, who is standing there?". (For example, as a followup question once the conversation has already established that somebody is standing somewhere else.)
Yes. Just like in English, where the question word is followed immediately by the verb. The reason is simple: the question word has the natural emphasis of the question, right? And, as such, it is naturally placed in front of the verb, ie. to the most emphasized position in a sentence.