The nuclear fissioning stopped when the control rods were inserted, and the reactor went subcritical.
They would normally let the core cooldown and depressurize before opening the reactor vessel, but they lost that cooling when the lost offsite power and then the emergency diesel generators quit after one hour. It would normally be a day or so before they start preparing to unload the core. But since they lost cooling, there was no cooling down of the reactor, and it would be unsafe to try and unload the core.
At shudown, the fission products are still generating heat from beta and gamma decay, and there are also some alpha-decaying transuranics. The heat is about 5 to 7% of operating power, but this quickly decays as the short-lived isotopes decay rapidly over a few days.
This provides a reasonable overview -
http://en.wikipedia.org/wiki/Decay_heat#Power_reactors_in_shutdown
I would expect TEPCO and the government to very cautious about what they reveal to the public.
In theory, they should be able to determine from certain radioisotopes whether or not the fuel in the core has been breached. Xe and Kr can be present in low levels from tramp uranium, or small breaches in the cladding. If there is Cs and Sr in the coolant, that could be indicative of fuel failures. If the detect Np-239, Ce-144 and other isotopes, this is a pretty good indicator of fuel failure.
The last I heard, the plant personnel were attempting to flood the containment with seawater in order to cool the reactor.
This shows the Mark I containment (from World Nuclear Net/GE) -
http://a4.sphotos.ak.fbcdn.net/hphotos-ak-snc6/183707_10150122455179029_53295319028_6446711_4177387_n.jpg
The will try to get water into the core which is inside the pressure vessel. I don't have any information on the integrity of the containment or the primary system, so I don't know if any of the recirculation piping has been ruptured. The steamlines go out of the upper portion of the reactor vessel, but steam line valves isolate the primary side from the turbines when the plant is shutdown.