Thermal dissociation of hydrogen and oxygen in water would still indicate pretty high temperatures. What is the minimum temperature for that to occur and does it exceed the melting point of the cladding? If so, then yes, some or maybe all of the hydrogen could be generated in that fashion.
Yes they need to keep coolant levels up, no disagreement there. Thats probably why they are using sea water. Because the rest of their coolant supply is probably gone.
One article I read said the temperature for the hydrogen/oxygen was about 500 deg C along with some level of elevated pressure. Not sure what that pressure is.
The cladding melts at around 2200 degrees Celsius. They only experienced this on the parts of the fuel rods which became uncovered by coolant. The fuel itself melts at around 3000 degrees.