How long does a supernova last? Is a supernova over instantaneously? Or, does the (for want of a better word) explosion continue for a while? What is/are the order of timescales involved? What is the duration for which the supernova continues to release copious amounts of energy?
 A: If you're asking about the duration of the explosion of supernovae, then it's done within a few seconds (the number can still be less) - similar to a nuclear fission. But, the cloud surrounding the explosion (i.e) the matter remnant that is thrown off can still remain expanding for years and it can emit EM radiation in the form of $\gamma$-rays and X-rays which can be detected. This result has a similarity with that of the big bang. The historical light from the big-bang (thought of as) is still detected in the microwave region due to redshifts. For example, SN-1987A has been observed by the Hubble for over 15 years and there's a time lapse sequence for the explosion in Wiki...
(In case of atom bomb, a mushroom-kinda cloud is formed which expands slowly and so, the matter can cover high altitudes, which can be easily tracked by GPS satellites)
A: Supernovae can take well over a week to reach maximum luminosity, and they stay rather bright for months after the peak. This just goes to show how much energy is involved in these event.
I was going to assemble a collage of light curves from my own research, but then I realized this has already been done at Wikimedia Commons:

These are rather idealized curves, but they do get the point across. In all cases, the ejecta is expanding at thousands of kilometers per second for most of the process. As the cloud of material thins out, its opacity drops and it is less able to heat up from any energy deposited on its interior surface. Add to that the fact that freely expanding gas will cool (think of air being let out of a pressurized tank).
In order to glow for so long, there must be an energy storage mechanism at work, slowly depositing energy into the gas so that it can give off light. For Type II supernovae, part of this energy is the latent heat of ionization of hydrogen - most of the hydrogen was initially ionized, and the electrons slowly recombine with the protons, giving off photons. Type I supernovae are defined as not showing signs of hydrogen in their spectra, so clearly this won't work. Instead, especially for Type Ia, energy is primarily obtained as radioactive byproducts of the original explosion decay. The most important decay chain is
$$ {}^{56}\mathrm{Ni} \stackrel{\text{6 days}}{\longrightarrow} {}^{56}\mathrm{Co} \stackrel{\text{77 days}}{\longrightarrow} {}^{56}\mathrm{Fe}, $$
and in fact some of the slopes of the piecewise linear Type Ia light curve can be attributed to these half-lives.
A: I love theoretical physics, I am not capable of the math, but here's a neat comparison. This is one of many proposed solutions to the mean free path of a photon produced in the core of the sun, this one says 4000 years to travel to emission surface...pretty wild drunken walk indeed! This is due to the assumed density of the core and various assumed layers making up the solar structure.
http://image.gsfc.nasa.gov/poetry/ask/a11354.html
SN1987A was several solar masses. The equations relevant to this phenomenon come up with...somehow, a kinetically powered explosion lasting a few days, which manages to propegate through several solar masses of matter. 
All things being equal it would seem that a core collapse supernova explosion for a several solar mass star should take alot  longer to manifest visually.
