Respectfully, your response is riddled with errors.
First, there’s a lot more to reactor design than “just putting fuel rods next to each other and they heat up.” The fuel rods are inserted into fuel assemblies which contain somewhere between about 60 and about 200 individual fuel rods. The fuel assemblies are then inserted into the reactor when it is shutdown (the Canadian CANDU reactor can be refueled while producing power). A reactor core will contain between about 120 to more than 800 fuel assemblies.
Postulated accident scenarios are analyzed prior to insertion of the fuel assemblies.
The temperature is not kept in balance by a super-heated coolant. In a pressurized water reactor (such as is being constructed in China, South Carolina, and Georgia), the water is pressurized to 2250 psi and is kept in a liquid state. The heat in the coolant is transferred, as you write, to water in a separate circuit at lower pressure where it does boil to steam which then powers the turbine-generator.
In a boiling water reactor (such as that used at Fukashima), the system is pressurized to about 1000 psi and the coolant boils at saturation temperature in the core and goes directly to the turbine-generator.
A meltdown does not occur when the fuel rods are so close together for too long. The fuel rods are fastened in the fuel assemblies and do not move. A meltdown occurs when the coolant is lost. The reactor is already shutdown, and the fission chain reaction has been shutdown.
While recriticality can in principle occur if a core melts, I don’t think that we have actually seen one.
In an emergency, the reactor is “scrammed”, which means that the control rods are inserted. No fuel rods are dropped. I have no idea what “flood the coolant” means? If certain sets of instrumentation responses are received, then a “safety injection” is triggered in which the reactor vessel is flooded with additional coolant due the instrumentation response indicating that the coolant system has a leak.
A reactor scram can be automatic or can be manually actuated. If it is a manual scram, then you are correct - a button (large red) is pushed and the control rods (in a pressurized water reactor) dropped in due to gravity. (The control rods are inserted from the bottom of the core in a boiling water reactor and are hydraulically driven).
Your final question is based on a misunderstanding of how a reactor operates.
When the uranium or plutonium fissions, it typically splits into two isotopes, both of which are radioactive. Their radioactive decay produces heat, which must be removed. When a reactor is shutdown, the fission chain reaction is immediately stopped, but this decay heat contiunes - when the reactor shuts down, the decay heat is about 7% of the power immediately before the shutdown. The amount of decay heat decreases with time. A meltdown occurs when this decay heat cannot be removed.