They have been located and identified as such by astronomical techniques.
Yes. To date scientists have discovered well over a thousand planets orbiting other stars. It is believe that a large portion of the stars in the night sky have planets.
Yes. As of August 2015 scientists have discovered nearly 2,000 planets orbiting other stars.
The planets are considered moving around the sun, even though the sun moves too (in tiny circles opposite the planets' motions). The planets are circling the sun. The sun (dragging the planets along with it) is circling our galaxy's center. Our galaxy (dragging the sun, the planets, and all the other stars) is moving through the universe as well.
Scientists (astronomers) can and have seen planets going round stars other than our own Sun.See related link below.
In our solar system, the planets Jupiter, Saturn, Uranus and Neptune are more massive. There are over 300 extra-solar planets known to be circling other stars; in most cases, only very massive planets can be detected at such ranges. It is likely that other smaller planets also exist, but we have no indication of that so far.
not a clue
You can find the names of some 260 different stars with planets circling them here: http://exoplanet.eu/
Currently scientists are finding many new planets every year orbiting other stars.
Stars wobble due to the gravitational influence of the planets orbiting them. As planets orbit their stars, their gravitational pull causes the stars to move slightly in response. Scientists can detect this wobble in a star's position, which provides information about the planets orbiting it.
Both new planets and stars are being formed. Scientists are actually watching the formation of planets and keeping track of which ones would be able to support life.
There is probably nothing unique about our solar system. Scientists once thought that planets might be rare, but we're finding that planets appear to be as common as dirt; we know of over 400 "exoplanets" circling other stars. So far, our technology isn't good enough to locate a planet as small as Earth, but with big planets as common as they are, there's no reason to think that "ordinary" worlds will be any more rare.
Scientists used to wonder; are planets rare, or are they common? Arguments went both ways. But over the past 10 years or so, we have discovered over 300 planets orbiting other stars. With the rapid improvement in space-based telescopes and better image processing software, it begins to look like planets, and planetary systems, may be the norm; that single stars without planets may be the unusual case.