1) No
2) Two different developers. 13Versus is an action RPG by the kingdom hearts team for PS3. 13Agito is an action RPG for the PSP. Not sure what team but Nomura is somewhat involved in this. Regular FFXIII is a tradition RPG for PS360. It's turn based but not quite like FFVII. Much more fluid. Being made by the final Fantasy 10 team. So yea, 3 different Final Fantasy XIII's being made. All have differen't stories and characters and settings. But they just happen to take place in the same Universe.
3) Final Fantasy's aren't in a continuing story. Each one is a different RPG series in a way. The only sequals are Final Fantasy X-2 which is a sequal to X. A sequal to 4 but on Cell Phones and WiiWare only I believe. Pick up the next one, you won't have to worry about missing out on any part of the story. It's not Metal Gear or an entry in the Saw Movie Franchise, LOL.
4) Which ever one has the sexiest trailers to you :P. However it should be noted that we don't no much about VS13 yet. And it's also the only one we haven't seen gameplay for yet.
4 ≈ One
