Most orthodontic treatment will have a set fee based on your complexity and every step has an associated charge with it part of the set fee decided on. Every office has a different payment plan which they would review with the patient. No reputable dentist/ orthodontist would do work...
I personally like to have a frenectomy done after orthodontics (whether you use braces or Invisalign). The reason is that when you do any type of surgery, you are going to have some scaring occur. I would rather have that scaring form around teeth that are closed versus open. ...
If you have agreed to proceed with treatment and the doctor has taken impressions for Invisalign, he/she has provided a service and incurred expenses in doing so. It is perfectly proper to be charged and be expected to pay for it if you change your mind. This might be a few hundred...