I would guess there is a pixel width limit between logo and txt name for when it pushes the rest of the space over.. Think that the post count in threads uses that space and needs a certain amount.
Ah I see what you mean. Yes, searching requires a logged in account (unless set to allow guest searching in ACP), but there is no dedicated "search" page, I suppose...
In the ACP you can give the image a class. Use cover to have it fit the box. Or you can give anything you want and then customize in the theme CSS override.
