Indirectly, it can help your homepage a little. However, in general, the page that is linked to is the page that will receive the most SEO benefit.
So, If I want my homepage higher in the SERPs, I should continue backlinking my homepage rather than deep linking?
It depends. I like to build backlinks for both the homepage, as well as many inner pages where the best content is located. In the long run, you find that you'll get most of your CTAs (call to action) by having a great many pages that do well in SERPs rather than just having one (the homepage). For example, if I have a homepage that provides 1000 unique visitors per day, where the inner pages provide nothing, I ultimately do less volume than if I have 10 pages of really good unique content that each provide 200 unique visitors. And it may seem like that's more work, but ultimiatly, once you hit that wall in the SERPs (and you will) you'll see that it's actually easier to get 10 pages with 200 unique visitors than it is to get that one with 1000. Try to concentrate on providing high quality content, then promoting that content, where ever it may be within your site.
it will help to support your homepage if the internal pages have pr and they link with anchor text to the homepage. but you better build links t the homepage
as far as I know - deep link (a link to an inner page for your site) is beneficial for that referral page mostly , for the home page, at first you have to make some direct backlinks to the home page, after that you have to make some link wheels.
It does help over time. By deep linking your inner pages, the links back to your home page become stronger (you do have a link to your home page on those pages, right?) Inner pages also give you a more realistic link building portfolio as well as giving you a better shot at long tail keywords.
If you have a good internal linking structure and funnel your internal linkjuice forward to the main page.
It helps the search engine locate all your pages more easily if they are linked to within your posts etc. Also, if you're using keyword linking it might help a bit as well.