Is there a way to edit the code of pages/posts that were created
inside the CMS (user clicks “new page” instead of manually creating a
file like a normal site) or am I limited to working within WordPress
itself?
Not really. The markup for pages is determined by the templates in the theme. What goes into the content editor is just one part of the final page. You should review the WordPress Template Hierarchy to see how WordPress determines which template to use for which pieces of content. Then you’ll want to review Template Tags to see how to pull in content from the back-end into templates. If you wanted to manually edit the code for all your content, then you shouldn’t be using a CMS. The CMS is designed to abstract that part away from the content.
What is the easiest and most efficient way of getting a live WP site
to local? I’ve tried BackupBuddy (has its issues), Wp Clone (currently
found it easier to backup the DB, and FTP from live to local with
large sites)
You’re just not going to find a single best answer for this. There’s many approaches you could take and they all have their upsides and downsides. You’ll just need to evaluate all the answers you do find and decide which best suits your needs.