Is it possible for a galaxy to exist or form "Below" our own?

There is no "up" or "down" in space, actually. From having the same orientation as we use on Earth, the Sagittarius Dwarf is actually "below" the Milky Way. However, again there is nor up or down and satellite galaxies are orbiting the Milky Way in all directions. The Andromeda Galaxy formed close to the Milky Way in the early universe but they are 2.54 million light-years apart now and are travelling side by side bound by gravity. Galaxies don't form now. The universe's past that age.

Clear skies!

No. On local scales, the expansion of the universe is trivial. IE the distance between our local group of galaxies and other nearby groups is only increasing at a very modest speed. And even then, just because there is new space, galaxies have to form out of something, and the expansion of the the Universe isn't adding any new material to the Universe.

http://en.wikipedia.org/wiki/Local_Group

In essence you are asking if there is any way for a new galaxy to form near the Milky Way. The answer is yes. In fact at some point the Milky Way and the Andromeda Galaxy are going to hit each other or have a near miss, at that point clouds of gas and debris will be ejected and new smaller galaxies will form.

So yes, galactic formation is still going, but what new galaxies are formed are made of remnants of old galaxies. This has nothing to do with the expansion of the Universe though.

http://en.wikipedia.org/wiki/Galaxy_formation_and_...

Very loosely. Which direction is "below"? There is no "outward" direction or center, the universe is expanding everywhere in every direction. There are galaxies of all ages in every direction we look.

Some galaxies are merging with others, but I think that very few galaxies are forming at this age of the universe. The youngest known galaxy (I Zwicky 18), is ~ 500 million years old. But most galaxies are older than 5 billion years.

The term "below" is totally meaningless except in a gravitational field, such as on the surface of a planet. There is no "below" our galaxy. Millions of galaxies exist in every direction from our own Milky Way Galaxy, so any direction you go, you will encounter countless galaxies.

I'm not sure I understand your question or what it has to do with the expansion of the universe. Our galaxy exists in three-dimensional space, and there can easily be objects above, below, left, right, ahead or behind it.

There are already several galaxies all around the Milky Way. This is called "The Local Group".

Additionally, the Milky Way is already "eating" a dwarf galaxy that has collided with the Milky Way.

http://uanews.org/node/25687

http://news.softpedia.com/news/The-Milky-Way-Eats-...

http://en.wikipedia.org/wiki/Local_Group