Hi,
#1. Search by title book and author name: I see you use Advanced Woo Search PRO plugin, and now this plugin is working properly according to your requirement.
#2. Sort by book creation date:
pa_im-ekdosis are taxonomy attributes that you create, WordPress doesn’t have a query to sort by these taxonomy, so I had to move this config to post_meta ( custom field) to be able to sort products by book creation date.
I also checked your pa_im-ekdosis, the format you are leaving is year/month or year. I have to convert your attribues to timestamp format so that they can be compared and sorted by book creation date. So when creating a new pa_im-ekdosis, please put the correct year/month or year format.
I have done custom sort by book creation date in sort filter on page shop and page category. You can choose this option to sort by book creation date: https://prnt.sc/tByFSwWOpUIw
Please recheck and let me know if you need to help.