We have plans for improving the notes feature (including making annotations available in the Paperpile interface), but are still debating what other changes to include.
As for your second request, you can copy your bibliography and notes to your clipboard (and paste them in a document) by selecting the right Citation Style. With the correct citation style, select the papers in your library and press the Cite button (or Ctrl/Cmd + C).
For notes, use “American Psychological Association 6th edition (annotated bibliography with personal notes)”
For abstracts, use “American Psychological Association 6th edition (annotated bibliography with abstract)”
For both, use “American Psychological Association 6th edition (annotated bibliography with abstract + notes)”, which I have attached here: apa-abs-notes.csl (22.6 KB)
To add it, go to the gear in the upper right --> Settings --> Citation Style --> Upload CSL file.