How do I best optimize my on-page SEO for a magazine-style wordpress theme?

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My Wordpress website is set up with a magazine style theme (Newspaper). Maybe that's the issue overall here. Questions:

1) Pages vs Categories vs Posts

I currently have a category with a few dozen posts under it. The category page itself has a ~1000 word article on it. It paginates every 10 posts or so at the bottom, but most of the page is duplicate because it's only swapping out a few links.

Should I instead make the "category" a page with the posts childed under it? What's the best way to go about that?

2) Canonical and Pagination

I get errors about a ton of duplicate content for paginated categories and my author page (all posts are under the admin account, which has ~40 pages or so. Every page is just a list of posts and it bitches about duplicate Titles and Descriptions on every one of the paginated posts). Should I canonical these back to the root author? Same question regarding pagination for categories, assuming I'm not going to be switching them to Pages.

3) Home Page Links

Right now my home page just shows a few links to the top posts of all time. After that, it shows the 5 newest posts. On the sidebar it lists a few random pages/posts. There are also a few "category listings" which just shows random posts relevant to that category. Do I want something more static/structured? The navbar does list most main content pages under their appropriate category, but the home page itself is pretty much dynamic.

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Thank you for the response. I ended up disabling pagination on the category pages (as there aren't  more than 20-30 posts per category) to fix the duplicate content issues caused by paginating each page 5-10 times with the same 1000 word article on each page.

I then fixed the author page Titles and Description issue by adding some dynamic tags provided by Yoast in the Author page. Simply changing it from "All Posts by (Author) - Site Name" to "All Posts by (Author) - Page 2 of 36 - Site Name" dynamically, it fixed the duplicate titles completely. Same with the meta description..

As for the home page links, I changed the linking structure entirely. Instead of random posts per category, it now has a link to each category page with the 5 most recently added articles per category under them with a link, image, and text snippet so the page will be more "static" for a while and provide some link flow to my new content, but still update as i add content. I then moved the top 5 posts of all time in the sidebar followed by the most trending article from the last 7 days (by view count).

Finally, I customized my 404 page to show the top 3 articles from my top 3 categories after reading an article about keeping your 404 page relevant and helpful to your viewers just in case I have a bad link come in.

I made all of these changes about a week ago and am waiting to see any changes in rankings, but I think, at least from a reader's viewpoint, the site looks much cleaner and easier to navigate. It didn't make a whole lot of sense to just randomly display whatever the theme felt like every refresh.

Thanks again!