This isn’t a WordPress issue itself.
I understand you want the whole site’s content but that requires a lot of work or else access to the raw site and the ability to configure the donor site to give you what you wish.
You have the sitemap to help guide you.
Maybe you might step away from a WordPress centric solution into the realm of scraping content then publishing what you want of that content. That isn’t easy but as there is nothing I can offer to do this from the WordPress standpoint I’d suggest starting out with some sort of mech such as HTTrack with some custom code to push the content into your website.
I’m going to step away from this thread as I’ve exhausted most of my knowledge in this subject as it pertains to WordPress… The other ways of accomplishing what you want would require some developer work and software outside of WordPress.
If I/We could help you through other WordPress issues or specific questions then feel free to ask.