While surgery can be done without orthodontic treatment, it's not ideal. When surgery is performed, the top and bottom teeth need to be coordinated in good alignment so they can fit together. If it's the braces you're worried about, surgery can be done with Invisalign being used to align the teeth and temporary anchorage devices being used during the surgery. These are also called mini screws. Braces give us the best control but options do exist. Best of luck!
With teenagers, cooperation can often be a problem when it comes to orthodontic treatment. The Blue dots fade while the aligners are being worn so an orthodontist can tell if the patient is wearing them enough. It's not a problem is one of them fell off. Just keep wearing the aligners.
Your crowding does not seem too severe to warrant tooth removal but without evaluating your bite and how the teeth look within your smile and face, a definitive decision cannot be made. Make an appointment with an orthodontist to learn more.
As already mentioned by other people here, refinements are no big deal. If you need them, you do them. It probably should have been mentioned at the beginning but it doesn't cost you or the doctor anything extra to do it.
Roughly speaking, Invisalign cost in the US is around $5000. Some charge more, some charge less...but $12000? That seems high. Your case is very complicated (appears surgical to me) and orthodontists can charge what they want based on the complexity of a case. If the orthodontist is a top invisalign specialist and can show you results, then perhaps it's worth the money. I for one, cannot treat a case like yours with Invisalign and obtain the results I want. Good luck.
