Some printers (such as newer HP models) have a feature like HP ePrint that allow you to print from any device via email.
If your 3TB device supports FTP or SMB, there are apps available for Android (like AndFTP or AndSMB) to allow you to copy files to and from the device or your Windows computers.
Answers & Comments
Search google play for these programs
"print"
"file server"
"ftp client"
"lan storage"
Some printers (such as newer HP models) have a feature like HP ePrint that allow you to print from any device via email.
If your 3TB device supports FTP or SMB, there are apps available for Android (like AndFTP or AndSMB) to allow you to copy files to and from the device or your Windows computers.