Regarding the delay you’re experiencing I can’t think of anything other than your servers resources, I suspect it’s php memory allocated.
Try the following remedy by adding the following two lines to your wp-config.php found at the root of the WP installation.
define( ‘WP_MEMORY_LIMIT’, ‘256M’ );
define( ‘WP_MAX_MEMORY_LIMIT’, ‘256M’ );
If this still shows you problems and would like us to take a look for you, please include a Temporary admin access and FTP access to the WordPress installation.
The CF Shortcode Widget, should work with any shortcode registered, please try a Contact Form 7 Shortcode as a test, and let me know any non-working shortcodes and we’ll test them out as well.
I’ll need the access to check out the Blog Sidebar for you, please include which sidebar you would like to show and the page name or url.