I would say the flowers are probably unnecessary, but not really inappropriate or weird.
As for your letter/questions, there is nothing wrong with that at all. I would recommend addressing it to the stage management staff. If you still have your Playbill handy you'll find their names there, or you can just do a general address to "*Name of Show* Stage Management" (I would recommend putting that even if you do have a name, just in case there was a recent staff change, the person you addressed it to is on vacation, etc). The response rate may vary, but as long as you are upfront in your letter about who you are (student, teacher, etc) and keep the tone of the letter respectful and don't come across as demanding answers, you'll most likely find a good number of people are open to answering as many questions as they can (there may be some things they can't disclose for a variety of reasons, especially if it's some sort of "magic" effect).