For example if someone links to http://www.yourdomain.com/gadgets/robotic-arms does the PR of ONLY that page increase? Or does the PR for the homepage, e.g. http://www.yourdomain.com increase also, as a result?
yes if you link from your inner pages to home page then that count as a vote form that page to the page which you link and thus this affects your PR..
yes it is...just like all you subpages to you index as possible and the PR from the subpage will affect the PR of the index page...