In FIFA 12, now that the game is finally the same on PC and consoles, is it possible to play against people on other platforms (XBOX, PS3) with my PC version or are those on completely different servers?
It's not possible at all. I can tell you for sure that the servers are totally different and the servers that host PSN and Xbox Live won't connect with each other due to PSN and Xbox Live being totally different consoles and companies. For example on the PS3 you can only connect with people using PSN so they must have to have a PS3. The EA ID is only for tracking stats that can be viewed online. As the comment above says it will only ever be Xbox > PC or PS3 > PC.