There are about a dozen threads on this in various forums.
These two seem most relevant to your first question:
What is the worst case scenario for Japan right now? (re: Nuclear plant)
Why was Chernobyl so much more of a disaster?
The graphite fire was a contributing factor, but the biggest factors were that Chernobyl had a terrible design, no primary containment, and poorly trained operators with inadequate experience who intentionally disabled much of the reactor protective equipment in order to conduct an ill-advised safety test.
Sure there is a chance of fire. If the fuel rods heat up enough due to inadequate cooling, the zirconium alloy cladding on the fuel elements and fuel rod casing can burn.
Yes, if there is a complete meltdown along with failure of the primary containment.
Also, another recent problem is partially depleted fuel rods from one of the other reactors that were stored in a storage pool. The 40-foot deep pool provides both cooling and shielding. However, the level in the pool may have exposed some or all of the fuel rods, which could lead to a fire.
Only one of the reactors used some plutonium (about 6% of the total) in its fuel source. The most prevalent fuel is uranium.