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No, a nuclear reactor would not explode solely due to the absence of people. Reactor safety systems are designed to shut down automatically in case of any abnormal conditions, such as the reactor overheating or losing cooling. The presence or absence of people would not impact the reactor's physical safety mechanisms.
No, a nuclear reactor cannot explode like a nuclear bomb. The design and process within a nuclear reactor are different from those in a nuclear bomb. In a reactor, the control systems prevent the conditions needed for a nuclear explosion to occur.
As of the most recent information available, reactor number 3 at the Fukushima Daiichi nuclear power plant is not in a critical state. The situation at the plant is being closely monitored, and any developments regarding reactor number 3 and the overall safety of the plant will be reported by relevant authorities.
A nuclear reactor can explode if there is a buildup of steam pressure, causing a steam explosion, or if there is a core meltdown leading to a subsequent hydrogen explosion. This can release radioactive material into the environment and cause widespread damage.
The number of fuel pins in a reactor will vary depending on its design and objectives. In one reactor that I worked with, I seem to recall 137 fuel assemblies, with four bundles each, with 62 fuel pins each. That translates to 33,976 fuel pins in the reactor, each about 12 feet long.