Yes, you can read library books on a 300, that was the reason I purchased that model last year.
Not sure what you mean by downloading library books via
Calibre?
If you are downloading them from the library, the initial file
most likely will be an .adsm file, which is a pointer to the actual file. To get the file, you need to use
Adobe Digital Editions, which will download the correct file, and decrypt the DRM so you can use it on your Sony. Your Sony will need to be recognized by
Adobe Digital Editions as well.
So, do you have
Adobe Digital Editions installed?