Yes, stars can exist outside of a Galaxy, but the majority are within a galaxy.
They can be outside a galaxy. For a start, stars formed within a galaxy can be catapulted out of a galaxy (when they come close to another star, and change their velocity as a result).
Generally older stars are towards the middle of a galaxy whereas younger stars are towards the edge.
I assume, that a) by Halo stars, you mean high velocity stars, and b) by disk stars, you mean stars that stay within the galaxy (Normal stars).Halo stars are usually very old stars that do no orbit the centre of the Galaxy the same way that our Sun or other stars in a galaxy. Rather, they travel in elliptical orbits, which often take them well outside the plane of the Galaxy.
Those stars except Polaris or the North Pole stars really orbit the Milky Way Galaxy but not Outside
Our sun, also known as Sol, is of average size as stars go. Much larger stars exist in our galaxy, as well as much smaller stars.
Outside our (Milky Way) galaxy.
They can be outside a galaxy. For a start, stars formed within a galaxy can be catapulted out of a galaxy (when they come close to another star, and change their velocity as a result).
We have no knowledge about aliens either within our own galaxy or outside of it. This doesn't mean they don't exist; our galaxy is simply too large, and we haven't explored even the closest stars - at least, not so thoroughly that we can be sure there are no aliens.
We don't know of any planets that aren't within the Milky Way galaxy, but that doesn't mean much; stars that are not in a galaxy are rare, and the nearest such stars are too far away for us to have any hope of finding any planets.
No. All the stars you see at night are in our galaxy, but outside of the solar system. The only star in our solar system is the one at its center: the sun.
Halo stars are usually very old stars that do no orbit the centre of the Galaxy the same way that our Sun or other stars in a galaxy. Rather, they travel in elliptical orbits, which often take them well outside the plane of the Galaxy.
Generally older stars are towards the middle of a galaxy whereas younger stars are towards the edge.
Stars, star clusters, distant galaxies, galaxy clusters, nebulae, ...
A galaxy is by a definition a group of stars. If there were no stars it could not be a galaxy.
Every galaxy contains stars, if that's what you mean. "Galaxy" means "big bunch of stars". No stars ===> no galaxy.
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.
If our sun did not exist the other stars would be little different from the way they are. The sun is just one of billions of stars in the galaxy. Many of the stars we see in the sky are larger than our own sun.