How can I work with highlighted text annotations from Good Reader in Preview?
Probably this is not possible with Preview, but there is another (free) PDF reader that allows you to do this (at least your first three points, don't know about converting into another annotation kind): Skim.

After you've opened your PDF in Skim, you can choose Convert Notes... in the File menu. Then you have all your notes from Goodreader in the drawer panel on the right.