If you are doing minor tweaks to layouts, you may be better investing in a page builder plugin like Elementor or something similar to make small edits without modifying the overall theme and it will give you some drag-and-drop functionality.
Right now, I’ve set up a local site folder in Dreamweaver and tried connecting via FTP to the live site, but it’s a mess. PHP files either give errors or show blank pages, and Live View doesn’t really render anything. I also don’t have a local server running yet, no MAMP, WAMP, or XAMPP, and I haven’t set up a staging copy.
If you don't have a local server for testing, then you are putting your site more at risk then just editing pages on the server. Without a testing server, whether be it local or in a remote location, then DW will only have access to your live site meaning that you would only be updating your live environment.
In order to have a proper testing environment, you need to move an exact replica of your site including HTML/CSS/JS available via a file manager/ftp, as well as your mySQL database which stores much of the key data for Wordpress to display.
Once you have a testing server setup, you will setup the testing environment, like you do the remote FTP to your live environment, and DW will use that for its Live Preview functionality to pull from your test files and database.
So in your example of CSS not updating, I am suspecting that you have not uploaded the changed CSS file(s) back to your live server to see the updates. In a true testing setup, you would preview the changes on your testing server and if you like them, you would then proceed to push them to your live environment for visitors to see. This keeps your live environment safe while you are testing and allows you to make non-destructure changes to your website. In the case the updates were bad, they would only impact your testing environment and you could either roll back the changes and test others, or pull a new copy from your live production environment.
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