Hi Gregg,
Please find my answers from your inquiries below.
1) If I use the Article Duplication Plugin to create Joomla articles, are you able to direct which categories they should be put in?
Yes you can. You can find the settings from backend > plugin manager > easyblog - autoarticle > default article's category,
http://screencast.com/t/MZD0e2p8JlB .
2) If after creating a blog post in EasyBlog which creates a new Joomla article, I decide to delete the Easyblog post, will this delete the same Jommla article?
Since the post created from easyblog is actually stored inside joomla content tables instead of easyblog tables, the post won't get deleted in joomla if you decide to delete it from easyblog. You can choose whether the post will automatically get unpublished or not once the post is deleted from easyblog.
3) If I have created a blog post in EasyBlog and then it auto-posts to Facebook/LinkedIn and I then delete the EasyBlog post, will the post in Facebook/LinkedIn be deleted too?
No, the post inside Facebook/Linkedin will still remain.