Hi there!
I manage to solve all three of the problems :D
Number 1 and 2 were related to the XML sitemap. As I said before I use yoast 's automatic sitemap and after a lot of digging and searching I understood what the sitemap was for, how to build one, what to include in it and how to send it to google.
I still have to wait a bit (for google to update) to see if I did everything right but I believe I did. my sitemap is smaller now and includes only posts (i removed the archives, tags and authors pages because they were resulting in duplicate contents).