Yes, we have discovered several.
Well, there are planets outside of the solar system, and there is one that is livable, but I don't know what it is called.
None. By definition , our "solar system" is everything controlled by the gravity of our sun. The planets, their satellites, asteroids, dwarf planets, comets, interplanetary dust, and man-made satellites are "within" our solar system. Any "planet" outside out solar system is just that - OUTSIDE of it.
A solar system comprises a star (or combination of gravity bound stars) and their orbiting planets. We think the majority of stars are solar systems an we have detected planets orbiting stars other than the Sun. However in the process of forming a solar system we believe that planets my be permanently ejected from orbiting their stars and flung off into interstellar space. These planets would therefore indeed be outside any solar system.
Yes more than you can ever imagine
In any solar system; that's what planets do.
They could, but as of now, no astronauts have travelled to any other planets in the solar system.
Within our Solar System, no planet has more moons than Jupiter. [See related question] Outside of our Solar System, it is any ones guess.
The Asteroid Belt has no effect on any of the major planets of our solar system.
Two of them
Mercury and Venus.
We don't know if it has any moons. We currently do not have the technology to detect moons orbiting planets outside of our solar system.
Mercury and Venus. They are the only planets without a moon.