How to add search bar and member avatar to header/banner space

Hi all, I accidentally posted this under Plug-in support yesterday so I am reposting this here in the appropriate forum.

In my attempts to keep my site as user friendly as possible, I'm looking to add a couple simple items to the area at the top of the blog next to the "Welcome back, user!" space. I know some people try to remove the "Welcome back, user!" but I'd like to improve that space. One item is a search bar under the "Welcome back, User!" space, and the other is the member avatar of the logged in user to the right of the "Welcome back, User!" This resembles Facebook a bit. For the avatar, I'm thinking it might have to do with this piece of code:

I think this would be a nice cherry on top to an already fantastic theme. I look forward to any feedback on how to get started! Thanks.