First, welcome to the KFOCI forum! I hope you've joined the club as there's alot more to offer than just what's here on the website.
It looks like you have a decent builder and there's alot there to work with. To answer your question, yes, the issue with door alignment is directly related to the floor installation. Henry J's, because of the large doors, need to have things lined up correctly before floors are installed or you'll end up with an issue like that pictured.
About the sagging doors, it's due to bad hinges. They are prone to wear because the doors are so large. Fortunately, hinges are available thru vendors in the club.
It also looks like someone started to build a hot rod because the firewall has been heavily reconfigured.
Good luck with the project...keep us updated!