“Is there a way to put the Logo in the div.inner section somehow?”
Yes, of course. You can open the header.php file and replace the
"<div id="brand"> ...</div> in the .inner section of the
<div id="overheader"> ...
“Is there a way to put a static logo in the slider container, i.e. Top Left corner?”
No, without some changes in the php files it’s not possible.