Hi, Coreman! Sorry to hear about your 600's screen problems. I sort my books by Read and Unread collections too so I appreciate your desire to keep that organization system on the T1. For the T1, the Reader Library software is no longer compatible. You have to install the new Sony software called Reader for PC. When you install the new software, it will tell you that it detects the old software (Reader Library) and ask if you want to import your books. If you select yes, then it will auto-import your old books and collections. This option is probably the easiest for you. If you select no, then you will have to manually add (import) your books and recreate your Read & Unread collections. I will warn you that the new Sony software is very diiferent from the old software. Many of us aren't that happy with it because it has less user control and wants to auto-sync everything.
Alternatively you could switch to using calibre to manage your books and use Read & Unread tags to create the collections on the T1. You could also drag-and-drop your books to the T1 through Windows Explorer. However, the T1 won't create collections from folder names. You would have to manually create the collection names on the device and then add the books to the collections.
No, the PRS-600 wall charger will not work. The connection on the T1 is different (micro-USB). The T1 will come with the USB cable and then you need one of those USB to wall adaptors. Or, many people use the charger from another device that they have around the house such as a cell-phone. It's a much cheaper alternative to the official Sony charger. Here is a thread on T1 chargers.
https://www.mobileread.com/forums/sho...d.php?t=151558