Do links to my other pages improve how my site in general looks to search engines? Or is it just that individual page? Thanks.
That's why sitemaps were developed. While you supposedly can not pagerank sculpt anymore with Google internal links still effect which pages get visited and crawled.
it will increase the popularity of the individual page not the home page......................or if you have links of your home page at the individual page then it may increase the popularity of home page also...............