I will need to compare the changed files against my current files. If I had made any modifications I will need to incorporate them into the updated files and upload?

Are these the only files that I will need to worry about?
Modifications should only be in files placed into folders named for your template.....Then of these, only those that have a new version will require you attention....
If there has not been a change in the core file you need to do nothing to your custom file
And the override system. I see a folder in my cart for overrides, is this where I'm supposed to be placing my customized files?
NO...See the tutorial on overrides
https://www.zen-cart.com/tutorials/index.php?article=36

And if not in the tutorial, the RULE is any folder where there exists a "classic" folder - - the files there can be overridden
Note: Just the Files & not the folders

I have been following the CAPITAL TEMPLATE system and just adding my customized files to this. Am I doing this right?
Don't know what the "CAPITAL TEMPLATE system" is???