No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
Usually when a permit is not taken to do alterations or add ons, the additional space is as though it doesnt exist. I wouldnt concern myself to much with the appraisal, I would concern myself more with the quality of work and if the work was performed by code by licensed personal. As an example, there is electric running through the rooms, how was the electrical work done? The a/c and heating units? If the work was performed by licensed personal more then likely they would have applied for the proper permits.
Another consideration for you... Lets just say you purchase home, and something happens such as a fire (hopefully never) you figure no big deal you have insurance. Well once the insurance company investigates and finds out the fire started upstairs, and the work was performed with-out a permit and licensed personal, you may have a very hard time collecting any money for any damages, including your personal belongings.