Some themes are designed to provide author bylines on posts and some are not. http://wpbtips.wordpress.com/2009/08/15/author-displayed-or-not/ When I theme does provide an author byline, the only way to not have it display is to purchase an annually renewable custom design upgrade http://en.support.wordpress.com/custom-design/ and use CSS editing http://en.support.wordpress.com/custom-design/editing-css/ to change that.
The Home link tab is the URL for your blog http://mariagranovsky.com/
What exactly do you want to do? If you provide more detail then we can provide the best way to achieve it. Do you want your visitors to click into your site arrive on the page for your posts as they do now or do you want them to click in and find themselves on a Welcome page?
The front page of the blog by default will display your posts (not pages) http://en.support.wordpress.com/post-vs-page/ in reverse chronological order, with the most recently published post on top. If you do not want the posts to be displayed on the front page, then you can create a static front page Welcome” for your site and a “Blog” page for posts. If you choose a static front page then you have to create two pages as I said above. http://en.support.wordpress.com/pages/ “ After you do that you go to > Settings > Reading and make the designation change and click “save changes”. http://en.support.wordpress.com/pages/front-page/