Are comets known to exist in other star systems? Are comets a feature unique to our Solar System? Or, are comets/cometary clouds detected around discovered/observed extra-solar systems too? If they were detected elsewhere, how do such cometary clouds affect discovery by perturbation of planets in that system ?
 A: It is unlikely that comets are a feature unique to our Solar System. Since comets are simply remnants of star and planetary formation, then anywhere stars and planets have formed would be fertile ground to expect comets.
Their individual masses are relatively very small compared to discovered planets. For example, Halley's Comet has a mass of roughly $2.2\times10^{14} kg$ compared to roughly $6\times10^{24} kg$ for the Earth. That's a factor of 30 billion times smaller... so it is also unlikely that the same techniques used to discover Earth-sized or larger planets would find comets, too.
However, although they're not likely to be detected, given their prevalence in our planetary system, and given that they form from natural processes, and given observational evidence of other planetary systems, it is not unreasonable to infer their existence in other systems.
A: Astronomy -- especially exoplanet science -- has gotten very good at detecting impossibly faint signals.
In this case a very recent Nature article, Two families of exocomets in the β Pictoris system, claims to see thousands of exocomet signatures in the not-too-distant β Pictoris system. This is a very young system with an edge-on debris disk -- essentially a hotbed for the formation of planets and comets and other such bodies. This same group has made a similar claim for another system: Exocomets in the circumstellar gas disk of HD 172555.
In both cases, the technique involves looking at very high resolution spectra of starlight. This employs the same echelle spectrograph used in a number of radial velocity surveys. However, they are not looking at periodic radial reflex motion of the star itself, since this would be far, far too small to see when caused by comets. Instead, they look for anomalous absorption features near the calcium H and K lines of the circumstellar disk. They interpret these as Doppler-shifted absorption of comets passing in front of our line of sight to the star.
Actually, these claims have been made by others. See for example Circumstellar Gas-Disk Variability Around A-Type Stars: The Detection of Exocomets? where they looked at a population of A stars and saw similar variations in some of the young ones.
The reason this idea works at all is that even though comets are small they can be surrounded by enormous clouds of material blocking certain wavelengths of light. Consider that when a planet -- even one as small as Earth -- transits in front of its star, most of the planet's mass is not helping to block starlight. After all, a centimeter of solid rock will more than stop all light trying to get through, so the remaining thousands of kilometers of planet sitting between the star and our telescopes is unnecessary. A much smaller mass in a more diffuse cloud can accomplish much the same thing.
Now these results are still preliminary, and certainly one can come up with alternative hypotheses to explain the signals. However, I think it is fair to say that the ability to detect comets around other stars has now been shown in several proofs of concept.
