1 - There is no batch copy besides just using CTL+C and CTL+V on individual items. I agree that it would be nice to have "sync metadata" command, like you do in Adobe Lightroom. For embedded metadata (EXIF, or Reel #s, etc) you can get 3rd party programs that bath edit the metadata.
2 - When you change the label in the project window and them drag the clip to the timeline, the clip name is consistent between both. When you change it in the project window AFTER placing it on the timeline, the clip on the timeline does not change. Same thing vica versa, changing on timeline does not effect project name. I always just felt this was a strange quirk, but see how having independent names might help.