I don't know about buying second hand books but there are plenty of places to swap books. The Sunrise and the Olive Tree in Chorio come to mind but there are plenty more. just ask around while you are there.
Recommended reading on Symi? Well, it has to be books about Symi surely
James Collins'
'Jason and the Sargonauts' is a humorous tale set on Symi.
All of Anne Zouroudi's 'Greek Detective' books are good and the first one,
'The Messenger of Athens' is set on an island that is suspiciously similar to Symi
(Anne used to live on the island).
Finally the new release
'Midas' by Dominic Ranger is a thriller set partly on Symi and many of the characters in the book are based on island residents. Read it while you're there and you can have fun spotting them.