Yes.

Backlinks give a certain amount of "pagerank juice" that flows trough your entire site. Every page on your website will get benefit from incoming links (if they are correctly interlinked)

For example if an inner page on your website goes viral or gets alot of high quality links, the juice from that page will flow across all the internal and external links that reside on that page. In the end, your whole site will benefit and your homepage will get a higher pagerank aswell. Proper internal linking is the key in getting the most out of it

what nossie said + getting links to internal pages is a good all-round strategy for building trust to your site.

Yes, but technically domains don't have PR, pages do.