The closest galaxies to the Milky Way are(in order of increasing distance):
Note: The first four galaxies are dwarfs, which are significantly smaller than the Milky Way. The two Magellanic Clouds are in orbit around our Milky Way. The Andromeda Galaxy is around 15% heavier than the Milky Way(I'm not very sure about this, but you can check in Wikipedia). The Triangulum Galaxy is around 20% lighter than the Milky Way(Not very sure about this also).
The Andromeda Nebula was created in 1967.
The duration of The Andromeda Nebula is 1.28 hours.
Which Nebula? Astronomically speaking, no it does not. In our lifetime, we will not come anywhere near to a nebula. If your thinking of the Andromeda Galaxy then - well expect galactic fireworks - but not for about 3 billion years. [See related question]
Galaxy
There is only one milky way, which is the galaxy in which we live, however there are many other galaxies such as Andromeda Nebula. :)
In space and time anything is possible. Within our lifetime, then it will not happen, however in about 2.5 billion years the Andromeda Galaxy will collide with our galaxy, the Milky Way.
Andromeda is not a star. It is a constellation. But it is also the name, given in short form, to the Andromeda Nebula.
Earth is IN a galaxy - as is the nebula.
The name "Andromeda" refers to a constellation, and is often used to refer to the perhaps-misnamed "Andromeda Nebula", which is actually another galaxy, called M31. Charles Messier was a French astronomer of the late 1700s. His primary interest was in finding comets, but he kept finding things that LOOKED like comets, but turned out not to be comets. So he published his "Catalogue of Nebulae and Star Clusters" so that other would-be comet hunters would be able to easily determine that this comet-like object wasn't a comet. It turned out that the Messier catalog included many items vastly more distant, and more interesting, than mere comets. The Andromeda Nebula, or the Andromeda Galaxy, was item #31 on Messier's list. Canis Major is another constellation.
Some nebulae that can be seen without a telescope include the Orion Nebula (M42), the Lagoon Nebula (M8), and the Andromeda Galaxy (M31). These objects are bright enough to be visible to the naked eye under dark skies.
A Galaxy is far bigger than a nebula.
The solar system definitely is, and most of the stars you see are as well. If you can see the Andromeda Nebula on a very dark clear night, that is a system of stars outside our galaxy.