When you are working with FFXIV (at least on V1.0), there are Square-Enix accounts (SE account), and there are Final Fantasy XIV Service accounts (Service account).
A single SE account can have up to 8 Service accounts linked to it. A single Service account can have up to 8 Options (Characters) in it. That would be a total of 64 characters across all Service accounts on a single SE account.
You can login to ONE and ONLY ONE character within each Service account at a time, but you can also login to one character from each service account within the SE account all at the same time. That's 8 simultaneous logins at a time if you have the maximum 8 Service accounts on the SE account.
This is very much like FFXI except the Service account is called a PlayOnline account for that game.
However, unlike FFXI, you MUST have a registration code for for each platform you wish to play on for a given Service account. So if you wanted to be able to have the maximum 64 characters all playable on both PC and PS3, you will need to buy 8 PC registration codes, AND 8 PS3 registration codes. One of each needs to be applied to each Service account. This was not necessary on FFXI as that game could be played on any supported platform (PC PS2, Xbox 360) once the PlayOnline account had been established. (It is necessary to use a separate registration code to create each PlayOnline account, but it was not necessary to add any more registration codes to play on a different platform for FFXI)
Note also the maximum number of PlayOnline accounts within a SE account is 10, but for FFXIV Service accounts, it is only 8.
The OP may wish to consider applying the PS3 registration code to the main existing FFXIV Service account that you already have in order to play your main character on either platform. If you make a new Service account with that registration, you will only be able to play the characters on that Service account on your PS3. The others (including your previous main character from V1.0) will only be playable on your PC.
Applying a new registration code to either an existing Service account or to make a new Service Account will do nothing to the current "Active" status of the existing Service accounts. If they were active before, they will still be active after. If they were cancelled before, they will still be cancelled.
Also, at this point, there is no way to apply your CE code to anything. All code registrations are disabled until ARR goes retail at which point things may look quite different than they have with V1.0. But I suspect the structure of it won't really change that much.... just the appearance.
As for Alpha and Beta testing: there are additional "permanent" options listed at the bottom of the page (you may have to scroll to see them) on the Options page for each and every Service account. The markings that allow you to do the testing are placed there by SE. In the case of the Alpha test, they only mark one Service account. It is probably always the one called "Final Fantasy XIV 1"