the whole point of thematic (imo) is to provide a solid, constantly maintained, foundation.... you are free to make all kinds of changes to your theme, but since you don't touch thematic itself, you have to learn a new way to interact with it... ie hooks and filters. this is kind of a pain at first and so thematic has a definite learning curve.
there are probably not specific posts on how to do this b/c what you are asking is accomplished by removing and adding functions from/to action hooks.
if you take a look at:
http://bluemandala.com/thematic/thematic-structure.html
you can see the order of the functions in the thematic_header function. you don't want a blog title... well thematic_blogtitle() is responsible for generating that, so you'd want to remove that action.
function remove_stuff(){
remove_action('thematic_header','thematic_blogtitle',3);
}
add_action('init','remove_stuff');
remove_action doesn't work on its own, so you must add it to the 'init' function which is called very early on in the sequence.
plus there are posts such as:
http://wptheming.com/2009/10/useful-thematic-filters/
which discuss adding search bars and logos. the twitter, rss, and other badges are just a matter of wrapping their code in a function, adding that function to one of the available hooks in the header and then styling its position w/ CSS.
function add_stuff(){ ?>
<a href="#">A link to nowhere</a>
<?php }
add_action('thematic_header','add_stuff',8);
pay attention to those numbers at the end... they are the priority (or order) the functions in thematic_header (other hooks can use priority too) get called in. in the above case i just inserted a link after the #branding div closed.