1) more search options coming soon
2) Book Grids are added to pages. There are plugins available to add pages to your sidebar (including one built-in with WordPress)
3) If you mean the cover size, that’s a setting when you create the grid. If you mean the text size, that is based on your theme. You could change it with custom CSS.
Oh, I just remembered. There are plugins that would allow you to search by custom taxonomies. You could use one of them to allow you to search by category or tag (or cover artist, editor, series, etc.)