1. Yes you are correct about moving the blog to /blog so you can get the DA value from the root domain. It also will help your root domain more to have the content at /blog b/c any links you generate to your content will go back to the root domain DA.
2. I wouldn't recommend switching from wordpress. There is just no business case (SEO-wise) for switching away from Wordpress. The Yoast SEO plugin makes on page optimization and technical seo for wordpress a no-brainer and the WP community support will more than make up for any advantages you might think of on a propreitary system.
3. Yes tracking on GA will be suffice. You may want to setup a custom profile to track just the blog content in google analytics if you have someone who you want to be able to view blog analytics but not the entire site analytics. Just a suggestion!
Sounds like you are on the right path, hope this helps!