here is a link to a good automotive pro quality
DMM.
On that page is a download link to the users manual, which can help you understand how to test, even before buying a DMM.
There are cheaper DMMs available, but sooner or later you'll migrate to a more capable DMM, especially with a 150cc and above scoot.
As to your questions, I have learned from experience that anything is possible when dealing with vehicles. In fact they will frequently make a liar out of you when stating absolutes.
You might want to take the fuse out of the holder, use a ScotchBrite from the kitchen to clean the fuse and the receptacles. Also, use a small wire brush to clean the battery cables and terminals, then after re-assembly recoat the cables with a light coat of Vaseline.