Cannot really understand the bulk of your questin, but I am getting the sense that you would like to have your appraisal refunded due to factual errors.
As a borrower, you have the right to submit a rebuttal to the appraiser, You may do this either directly or through your mortgage originator.
Your responsibility is to provide additoinal comparables that the appraiser may have overlooked or to point out salient features of your home that were not highlighted in the appraisal.
You may want to provide supporting documentaion with permits,etc.
Present this information to your appraiser. They will have about three days to respond, in writing, to your disputed items. They will have the choice to either defend their position or increase the value.
If the value is not increased, the appraiser will stand pat on their value and in writing will refute your documentation.
You should, then, have the right to pay for another appraisal. If that appraisal comes back at a higher value, then appraisal cost should be refund or waived. If the value on the new property comes in equal or lower, that value is used and both appraisals are your responsibity to pay.
Regardless, when you pay for an appraisal, you are responsible for the cost regardless of the outcome.