The mark on a Kestner shoulderhead doll is on the back of the shoulderplate. It is not unusual for part of the mark to be under the kid leather body. I have to confess that I am not always right, though, just by looking. Your best bet is to invest in some really good books. Another excellent source is The German Doll Encyclopedia by the Ciesliks, also costly.
Replaced wigs are ok if they are nice old mohair or human hair.
Bulky synthetic modern wigs are a no-no. Be sure that the new wig isn't hiding something. The size of the doll affects its price, too. Usually a very large doll will cost more than an average sized one. Look also at the leather around the shoulders.