Hello,
1/ As I can see, you’ve disabled Breadcrumbs for the Home page so the image is not visible. I’ve set Background Image for the Breadcrumbs via Theme options, so that logo will not be shown on other pages also.
2/ You’re welcome! 🙂
3/ It is sidebar. Go to Theme Options > Blog > Blog layout > Show Sidebar Only On Blog Page > On or Sidebar Position > Without.
Content of that sidebar you can change via Appearance > Widgets > Main sidebar.
4, 5/ I will answer soon.
Regards