Ben -
Let me try to clarify some of your questions; I haven't seen the sword, so am answering in a general way to your questions.
It is a real sword - it was made in Japanese by an actual swordsmith using traditional methods. Therefore a "real" sword.
Gimei - a false signature, someone (maybe recently, maybe centuries ago) decided to "enhance" the value of the sword by carving the signature of a famous smith. How does you know that? By comparing to known, authenticated examples of the famous smith's signature (mei). This has been a common practice for centuries and is one of the main reasons for shinsa -where knowledgeable experts can look at the sword, its characteristics, signature, etc and compare them to known authentic examples.
Polishing vs leaving in "found" state: this is just a matter of custom of the particular culture and collectors ethic. The Japanese like to see swords in excellent condition regardless of age or how found. Other collector groups, like German memorabilia, Bowie knife collectors, etc like to have things in an "as found" condition feeling the cleaning destroys part of the history of the object.
Hope this helps a little. Nihonto is a very complex and confusing area of collecting. I've been studying and collecting for over 30 years and still don't feel I know more than a baby in the field.
Rich S