^
"Na2O + H2O --> 2 NaOH",
Nope. Elemental metallic sodium. You forgot the H which is evolved:
Na + H20 ---> NaOH + H
The monatomic hydrogen instantly combines with another monatomic hydrogen to form H2. There may be intermediate reactions, but that's the long and the short of it, starting from the metallic sodium.
There is a lot of heat involved in this whole process and the gaseous hydrogen ignites, causing the fire. The reaction is so fast and violent that unless a large heavy chunk of sodium is involved, it will "float" on the water because of the gas generated under it. The sodium will bounce around on the surface, causing a sizzling noise, unless it is a rather large piece. Like a drop of water on a very hot stove.
Been there, done that.