1) Having the username show up on each individual post is theme dependent. Certain ones do and certain ones do not. I use Regulus for a 22 author family blog and it works great. So you dont have to test every single theme yourself you can check out engtech's theme reviews as they are very comprehensive and have what you are looking for as well as plenty more info:
http://engtech.wordpress.com/tools/wordpress/wordpress-theme-reviews/
I do not know of any themes that allow for avatars showing up with the post they usually only show the username. I setup an author's page with links to their avatar and some info about them. If you want to link to their avatar then use this code:
<src="http://a.wordpress.com/avatar/username-128.jpg"/>
2) And to your second question yes to the fact that only administrators have the ability to change the setup of your blog. Here is a handy faq page explaining all of the differences between admin/editor/author/contributor:
http://faq.wordpress.com/2006/05/12/what-are-the-different-roles/