I will try and help as best I can but this is really wordpress programming issues.
Firstly get firefox and install firebug plugin. I use it is great!! When you right click on the thing you want to change firebug will actually tell you what files that ode appears in.
1) Your first question about removing spaces above header image :
remove the following code from header.php:
if( !dynamic_sidebar( 'above-header-widget-area' ) ) get_search_form();
and if that isn't enough you may need to delete some code in header.php that starts at line 23 but be careful editing this code as it could affect your on site SEO.
2)changing fonts is in style.css and starts around line 509
3) changing the width of the theme is also in style.css about line 186 you will see #wrapper and change the width 940px; to the size you want. However you will also have to play with the width of the following to make the theme look right.
#main (line 500 in style.css) it is 940px also and needs to be new value.
#primary, #secondary (line 78 in style.css) it is 220px and will have to be changed to the width you want for the sidebar.
I can't recommend strongly enough using firebug in firefox, it will change your theme modification life, if you aren't already using it.
Hope that helps.