Quasars

This is best answered with history. When radio telescopes were first turned on the heavens, point sources of radio waves were discovered (along with spread-out regions of emission along our Milky Way). Astronomers using ordinary visible-light telescopes turned toward these radio points and looked to see what was there. In some cases a supernova remnant was found, in others, a large star-birth region, in others a distant galaxy. But in some places where point sources of radio waves were found, no visible source other than a stellar-looking object was found (it looked like a point of like --- like a star does). These objects were called the "qausi-stellar radio sources", or "quasars" for short. Later, it was found these sources could not be stars in our galaxy, but must be very far away --- as far as any of the distant galaxies seen. We now think these objects are the very bright centers of some distant galaxies, where some sort of energetic action is occurring, most probably due to the presence of a supermassive black hole at the center of that galaxy (supermassive = made up from a mass of about a billion solar masses).

See the previous answer. It is thought the infall of matter into the supermassive black hole can result in very hot regions where huge energies are released, powering the quasar (i.e., producing the emitted light, etc.).

Well, the region of intense visible emission is quite small compared to the rest of the galaxy that it is imbedded in. The visible emission only occurs very near the center of the galaxy. On the other hand, huge regions of radio emission, produced by the quasar, can stretch out to large distances outside the galaxy.

The electrons near the center of the quasar can be accelerated to speeds near the speed of light. In the presence a magnetic field (which is present in these same regions), the electrons move along helical paths (paths that look like a stretched out slinky), and as a result, they emit radio waves (it's called synchrotron radiation, since these waves are observed on Earth when physicists send high energy electrons around in circles using magnetic fields, in particle accelerators call synchrotrons).

It appears galaxies may only act as quasars during the early stages of their lives, but it would still be for times of billions of years.

Nobody really knows, since we don't know exactly how they form! However, it can't take much longer than something like a billion years (the apparent answer to all questions about cosmology!).

See the above. But it's thought the process begins as gas collects near the center of a galaxy.

Not all that difficult, if you have a huge telescope! The Hubble Telescope, for example, is quite nice for various studies of quasars.

Probably, the only thing that would be left is the supermassive black hole. In other words, the gas near it would have been used up, and so the quasar shuts off. But the remaining stars, etc., in the galaxy as a whole (i.e., not near the very center of the galaxy), would, of course, still be there.

For one, they are only seen far away. Thus, since the light takes billions of years to get to us from a quasar, the quasars are all very old. There are no nearby quasars, so there are no young quasars; quasars are not made during our era of the universe, only during an ancient era. This also implies the universe was different place in the past (billions of years ago). It also says the galaxies we see around us now may have been quasars in the distant past; even our Milky Way galaxy may have been a quasar-like galaxy long ago --- now not much material falls into the large black hole at the Milky Way's center, so the radiation output from the center is not as great as it used to be.

No, they are extremely weak. The total energy collected by radio astronomers over the history of radio astronomy amounts to about the energy required for a mosquito to make one "push-up"!! The reason we don't receive lots more radiation is that the sources (e.g., the quasars) are so very far away.

That's not a well understood thing. It my have to do with the nature of the environment around the central black hole, the size of the black hole itself, and/or the orientation of the black hole and its surrounding, radiating disk of infalling material, as seen from Earth.

No, except that quasars are in galaxies of stars.

No real big difference. There are some "minor" differences having to do with time scales of intensity variation, and the presence or absence of certain features in the spectra of these objects.

A pulsar is a much smaller mass object, much smaller in radius and not a black hole, but a neutron star (it "failed" to become a black hole during its birth due to a supernova explosion of some single star). However, the neutron star is nearly as compact as a black hole of that star's mass. Magnetic fields near the blackhole and a pulsar may be similar in structure and have something to do with some energy output of each.