I then created a new page and set it to use that template.
Then I installed and activated the 'wp-minify' plugin hoping for it to drop the blanks and comments.
But when I look at the page's source code in the browser I see the code regularly.
Your advice will be appreciated.
As far as i understand WP Minify plugin works on scripts and styles that are included in your page
<head> tag as external files and not scripts and style that are in the
if you are inserting scripts and style in the
<body> tag manully you should insert it after you minify it and you can use many of the free online minify tools