The [same question was asked some minutes later](http://physics.stackexchange.com/questions/6956/what-is-generating-the-hydrogen-that-has-exploded-in-the-fukushima-reactor), but I saw that one first. 

1. Eutectic is quite irrelevant here, do You think that the uranium dioxide with some % of 
fission products happens to be a eutectic mix? The probablity of that might be calculatable 
with the aid of a bistromatic drive computer. Uranium dioxide melts around 2300 °C, the fission products will be only partly miscible with it, so I'd say melting point will be >2000°C

2. The Zirconium metal of the fuel tubes reacts with water vapor at elevated temperatures (above 1200 °C if I remember correctly) The reaction is simply: Zr + 2 H2O => ZrO2 + 2 H2 This is proof, that parts (at least) of the fuel rods were not immersed in water, but it does not prove melting.