Hi,
Regarding your issues:
please check the following article: https://demo.gavick.com/joomla25/john/index.php/typography/template-features (Menu features section). In you template settings -> Menu tab you can add IDs like blog or my-works to selected module position.
the header module should be fine now. I've added frontpage frontpage-header1 suffixes (template otpions -> Features tab) to your frontpage. If it's still not correct, please disable TinyMCE editor for your user and add the original header code again.
It would be much easier to install the quickstart package (joomla with modules, plugins, template, contend preconfigured) - in this case you'll have the same website like on our demo (only images are replaced), then you would remove unnecessary modules, edit other content etc.
Did you notice any error during News Show Pro installation?
Cheers
Joshua