Tablets don't generally show up in ADE.
You need to transfer files using a file manager instead to copy files to the tablet as a mounted drive.
Copy the .epub or .pdf files, not the .acsm token files.
(On Apple devices it is even more awkward, and you need to use iTunes, Dropbox or similar).
I don't know if the Nook app will read all Adobe DRM books or not.
Try the Bluefire app which I know supports Adobe DRM. Or Aldiko.
Also, the Overdrive app should let you download direct to the tablet and read library books; it's always felt a bit awkward for me though.