To see if things work, you will assign the new backend layouts to some pages. Remember that your default backend layout links to the "one content column with menu" content template. You have set the root page and all its sub pages to use this backend layout and corresponding content template for frontend output.
Click on Page, and then on the "1 column without menu" page. You will see that this page still uses the default layout (Content main (with menu)). Edit the page properties by clicking the page-with-pencil:
Click on the Appearance tab and set the "Backend layout (this page only)" to "Main 1 column without menu" layout:
Save and close. Remember, this layout is linked to the "main_1_column_without_menu.html" template file, so this will be used for the frontend!
For the next page, click on Page, then on the "2 columns without menu" page and then on the page-with-pencil icon to edit its page properties. Again, click on the Appearance tab and choose "Main 2 column without menu" for the "Backend layout (this page only)":
Save and close. Of course you can also set the "Backend layout (sub pages of this page)" box, but since your pages don't have any sub pages, it's rather pointless to do this. Anyway, do what you think is best.
Please note: if you use the layouts "without menu" for certain pages, these pages won't have a menu when visited on a mobile device. In other words: the user won't be able to navigate to other pages. This is due to the fact that the TYPO3Buddy tutorial once was desktop only.