In the screen shots you show an error that you are getting on the index page, you should not be going directly to the index page to view a gallery. Instead you should only have the include code on the page that you wish to see the gallery with. If you would like to go to the gallery directly you will need to use the URL that you see in the 'add to site' section of the PowerGallery Admin.
The end part of the URL might look like this:
index.php?gallery=1&theme=dark
As for the table that could not be found that you added manually I do not understand what is being stated here. If you have a connection to the db in DW then you should be able to see the tables for that db and make reference to them. Please explain this part further so that we can have a better understanding of the details.