I have seen Carmen at the Hungarian State Opera (NOT at the Erkel) and as a production I thought it was very well done. But I believe you are correct about your interpretation of the Erkel. Not that its bad, just that you are on a special trip and should capitalize on that in every way.
Oddly enough, I have also seen Miss Siagon at the Operett theater. Excellent production but you do know that there are some fairly raunchy moments in the story? I saw it with my wife and 20 year old daughter and was a bit uncomfortable. But I am pretty conservative. The Operett theater is very, very nice, but not the Opera House. One advantage of the Operett, if you can get box seats is that those in your box are taken into a parlor at intermission where you have a chance to share a table, hors d'oeuvre and Champaign with the other guests of your box. Since this is Budapest the odds are very good that you will be the only or at least one of the very, very few tourists in the room. We have met really special people and had great conversations at intermissions over the years. So the plus here is an intimate experience if you can find a box seat this late (first four boxes right and left of the center box).
I haven't seen Coppelia. But the Hungarian State Opera house is one of the top 5 Opera Houses in Europe; both the productions and the grandeur of the venue.
For November 1 you are also in luck. http://zeneakademia.hu/en/classic/-/program/budafok-dohnanyi-orchestra-en-20141101-1930 This performance is in the Grand Hall of the recently renovated Liszt Academy of Music http://www.resmusica.com/wp-content/uploads/2013/10/academie-franz-liszt.jpg . This is a stunning venue. I haven't heard a recital there yet but I have tickets for a performance in December. Can't wait.
Or if you prefer on November 1, https://www.mupa.hu/en/events/calendar/11/2014 This is in a modern but stunning performance hall http://www.hcb.hu/site/upload/2011/09/Bartok_Bela_Nemzeti_Hangversenyterem_p_p_51201007_m_mupa2.jpg
I am not going to start the argument of how to dress, but I do recommend that you look in the photos and see how the others have dressed and emulate them. Here are a couple of high resolution photos to assist
Hope this helps some