Deepak Gupta, DMD, MS

There is no way to know for sure how your remaining teeth will respond to the spaces created by your broken teeth being extracted.  Most likely the other teeth will gravitate towards that space and the teeth adjacent to that space will tip forward into the space over time.  It is VERY unlikely that your other teeth will move into the space of the missing teeth in a way that you will be happy with.  I would suggest you see your dentist or an orthodontist to find a solution that will work in your specific situation.

It is unlikely that the failure of the brackets is due to operator error since they tried to put them back on and the same thing happen again.  In my practice if a SINGLE bracket comes off we will take extra percautions to make sure that the field is isolated and no contamination of the tooth surface happens.  If several brackets came off I would expect the doctor to ensure that there is no operator error the second time.  My guess is that your daughter's teeth have atypical enamel which makes the brackets less likely to stay on or it could also be that she had a recent fluoride treatment at the dentist.  Fluoride can interfere with the chemical bond that is necessary for the brackets to stick to the teeth.  Waiting about a week and trying again is what I would do in this situation.  

That's normal. The permanent tooth that is ultimately going to go in that spot is bigger than the baby tooth that is currently there. The Invisalign trays take this into account and are going to create an ideal amount of space for the permanent tooth. 

I do not have any experience with SmileCareClub.  If what your orthodontist is charging you is too much you may want to consider shopping around.  Sometimes fees will vary considerably from one doctor to another.  If your case is truly just minor crowding then SmileCareClub maybe a descent option.  Only way to find out is to contact SmileCareClub and see if you are a candidate.

From the photos it appears you have excessive overjet (distance between the upper and lower front teeth) and not really an openbite.  To correct your overjet you could use braces or Invisalign but with either option you will need to wear rubber bands to pull you upper teeth back and lower teeth forward.  Another option to correct your bite could be jaw surgery or extracting one set of premolars in your upper arch and then closing the space using braces or Invisalign.  Which option is best for you cannot be determined just by the photos you provided.  Find a good orthodontist near you and they should be able to explain to you what your best options are.