If I build links pointed to subpages, is it helpful to increase the page rankor quality of our home page?
Little bit confusion in your que. If you are try to say that, if you target your inner pages than it'll or not helps your homepage to rank higher on search engines. Than it will help your homepage to rank higher. Not so effectively but will push. But I have one question that why you not targeting your homepage too?
What is the difference between: "having links to your overall site for all your pages" and "the links going to each individual page" please? I believe it is important to build links to inner pages as well as the home page, not least because if you can increase their ranking they will give additional potential for browsers to find your site.
It will push your website to get higher ranking definitely. Post good articles and extra ordinary content for your website, it will help.