if they were all shutdown as planned in Feb I doubt the outcome would have been that much different, possibly alot worse. the storage pools looks like the biggest danger to me, which would all have been packed with fuel. afaik 5 & 6s pools are most densely packed (and packed tighter than spec ...) due to them being offline.
To the best of my understanding:
1) You are correct in that there would undoubtedly still of been a large amount if not all of the nuclear fuel and material still on-site as they would of just begun decomissioning that would still need to be kept stabalized. However, real rough comparison here, lets look at a hot-live reactor that's reacting and generating much like a hot-running automotive engine. When it's on and running, it's really generating heat that needs to be disipated rapidly by the cooling system. However, unlike an automotive engine - where lets say you get a flat tire or something that requires you to suddenly stop your operation, you can pull off the road and turn off the engine and while off/inactive the engine doesnt need the assisted cooling further because, while warm, it is no longer generating heat and is in a gradual state of cooling - when the switch gets turned from on to off on a nuclear reactor it still has a TON of heat built up in it ontop of still generating some additional gradual heat. It still needs to be cooled with assistance at full power until it reaches a more stable tempurature and you're only needing to cool the more passive heat being generated while it's off. Normaly this is a process that doesn't take long, but at this plant when the quake hit, the three cores that were active shut down (while still really hot), and the coolant imediatley stopped being circulated.
2) The design of this plants is, I believe, of a taller stacked variety (an older GE design), with the spent rods being stored above, in a second-level, with the active reactor vessel and unspent fuel rods in the same "pool" of water/coolant stored in the lower level. This would explain why authorities have said that the main vessels themselves, with the worse of the nuclear material, are well safe (and submerged) in the coldest and deepest parts of these pools/tanks... the spent nuclear material though, which still has some strong radioactivity and is stored near the surface of these pools/tanks, is what the workers are having to fight to keep submerged, stable and cool (no water circulation, heat goes up and stays up from the vessels that were raging hot but have been gradualy cooling now).
It's a case where if they weren't active at the time, they would still have a warm pot of water, generating its own heat, to deal with managing and circulating some cool water into to keep stable. Instead they were active, so at the time of the quake, the pot of water was boiling-hot (with cool water being circulated into it and the hottest water being taken out to prevent it from boiling over) and the bottom that was sitting directly on the burner was glowing molten-red hot, and now the burner is turned off, but the bottom of the pot is still so hot it's generating heat, but now you have no water circulation so pressure is building, water is boiling away from the surface, and no fresh stuff is comming in to replace the water being boiled off or help reduce the temperature and pressures that are building.