All radioactivity decays with time. Some fission products from uranium fission will remain active for thousands of years, others decay to insignificance within a few years.
A nuclear power plant
Direct exposure to radiation from a plume of radioactive material
See the UNSCEAR report referenced as a link below
by a nuclear power plant
Water itself does not become radioactive, luckily, but any dissolved material in the water in the reactor primary circuit gets irradiated by the neutron flux and so can become radioactive. Therefore it is very important to control the water purity, it is all treated in a demineralisation plant, but then that is normal practice for power plants anyway, the difference in a nuclear plant is that the removed material can be radioactive. The secondary water/steam system in a PWR will not become radioactive, neither will the station cooling water used to cool the turbine condenser.
Basically a very long time. Most radioactive isotopes are radioactive for a long time. Uranium 232 has a half life of 69 years and plutonium 238 has a half life of 88 years. Some isotopes are very long lived.
6.25% will remain radioactive.
The Fukushima Daiichi nuclear power plant in Japan experienced a series of explosions in March 2011 following a powerful earthquake and tsunami. The disaster resulted in a significant release of radioactive material and led to the evacuation of surrounding areas.
Nuclear power plants can be decommissioned and shut down, but the radioactive waste they produce will remain hazardous for thousands of years. Accidents or meltdowns can release high levels of radiation and damage the plant, but the physical destruction of a nuclear power plant would not completely eliminate the radioactive materials.
NIMBY
Nuclear power plants release water vapor and steam into the air during the cooling process. Occasionally, trace amounts of radioactive gases can also be released, but these are carefully monitored to ensure they remain within safe limits.
The element that can stay radioactive for millions of years is plutonium. This is where most nuclear power plant energy comes from.