I'm looking at getting a 3tb WD red (NAS) drive and wanted to know if there are any hard drive enclosures with an Ethernet interface so that I can use it as a NAS system and just keep it plugged in and on all the time.
1. are there any enclosures like that?
2. will it work?
3. will I be able to access the NAS from outside the LAN, i.e. over the internet?
Nope, its designed to be used in a nas environment.
You router may have a usb port which may do what you want. You will need to check your routers manual to see what its capable of because some can and some cant and some of the ones that can won't share over the internet.
Other that that You might want to go with 'Cloud' edition drive, such as the Western Digital MyCloud drive,