The WP Latest Post Blogroll plugin creates a link with the most recent post title for each blog listed in the blogroll.
No. It is perfectly fine to have a mix of sites listed in your blogroll. Static sites will have the link name listed in the blogroll. Blogs with RSS feeds will have the title of the last post shown as the link name.
The name of the blog or website will be shown in the blogroll instead of the title of the latest post.
Yes, the categories that you select for your links will be honored. Each category is listed with the appropriate links given underneath. Blogroll is the default category for links and you can change that to whatever name you like.