After that you should be able to edit files you want.
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Does this mean I have to remove my current stylesheet and create/edit the new ones in my Theme Editor?
The current layout you have on your site, you can use that same stylesheet. You may have to go through pages such as index.php, comments.php, page.php, single.php and other pages to customize it to your liking.
Sometimes its easier for your first them to start off with the classic template. But I love the default more. If you have any other questions or need any help just ask.
The reason the files are different is because they all have different php includes. You can't just go delete that stuff. But sidebar template. Is just whatever .