To answer your question:

Yes, you can load two or three instances of the game (you could do this even in 1.0 with a bit of help >.>). If you want to make a new character with the code you get from a new copy of the software, it'll be an entirely new account, so another sub fee (standard, since its a brand new account and not Legacy).

If you decide to, you CAN link the new, second account to your SE ID, as it allows up to 8 service accounts. This has been true since the Square Enix account system has been in place. You're allowed to have multiple service accounts of XI as well.

The advantage to having them under one SE ID is being able to link them all under the same security token, and ease of entering SE ID/Passwords etc. Each account is able to log in on its own, regardless whether another account is already online.

You also have the option of creating an entirely new SE ID and linking your new account to that.It's free, so there is no detriment to doing it this way either. How you attach it to an SE ID is entirely up to you.

long story short: yes you can dual-box. Theoretically, you can log in to as many accounts as your pc could handle, and as many accounts as you have access to (I remember back in the XI heyday, there was this hardcore guy that loaded like 6 instances of XI to farm things like Dynamis and Limbus and all that lol)

I've dual boxed for many years on XI, and did it for a bit on XIV, so I'm no stranger to how SE has this all set up. Hope this has helped ease some of your confusion!