What I read tells me that as long as I have my page.php Template in place, and all my other Templates, and home.php or index.php is in the root WP directory, I can delete theme/index.php because it is just there for redundancy, correct?
No, you can’t do that. The index.php is the main file. It’s the fallback position for everything in the Template Hierarchy.
WordPress uses the Query String — information contained within each link on your web site — to decide which template or set of templates will be used to display the page.
First, WordPress matches every Query String to query types — i.e. it decides what type of page (a search page, a category page, the home page etc.) is being requested.
Templates are then chosen — and web page content is generated — in the order suggested by the WordPress Template hierarchy, depending upon what templates are available in a particular WordPress Theme.
WordPress looks for template files with specific names in the current Theme’s directory and uses the first matching template file it finds that matches the Template Hierarchy.
With the exception of the basic index.php template file, Theme developers can choose whether they want to implement a particular template file or not. If WordPress cannot find a template file with a matching name, it skips down to the next file name in the hierarchy. If WordPress cannot find any matching template file, index.php (the Theme’s home page template file) will be used.