Access the templates for this theme in your WP Console, under Presentation, then Theme Editor. But first, you must be sure that they are writeable by your server. In your FTP client, navigate to your theme folder, then CHMOD all *.css and *.php files in each theme (if you have more than one) to 766. Then you can edit them in the WP Console.
The file that has your sidebar and "About the Author" items is probably called sidebar.php. You can just add some text about yourself to appear where the placeholder text is, or you can delete it altogether if you want.
What the theme author is talking about is creating a separate WP "Page" for your About Me information. You can create all kinds of different "Pages" for not-often-changed items, e.g., Contact, About this Site, About the Author, etc.
As for the tabs at the top, they look to be hard coded. Once you set up your Pages, you can put them there, or you can hard code any other links there that you want.
It should be obvious when you view your sidebar.php file where the archives are. Just delete that entire little section.
Also, the only way to avoid the content spilling over into the sidebar is it is on that one post is to edit your link and not make it the entire URL, but enclose it as follows:
<a href="this.is.a/very/long/URL">Short Description</a>
Then it won't hang over the side.