While the Gmail interface is generally very simple to use and understand, it makes it a bit of a nightmare to work on large numbers of emails at the same time, unless you know a couple of little tricks.
To make managing your inbox easier, Gmail allows you to search for emails and select multiple emails at once. Even if you need to save more than 50 or 100 emails. And you can save them to PDF, save them to Google Drive, etc.
And here is the trick how to save all emails matching your query or filter to PDF.