|MadSci Network: Astronomy|
First of all, you (and your parents!) should know that "Star Registry" companies-- i.e., people who "sell" star names-- are not official scientific organizations. It's a nice gesture, but only the International Astronomical Union (IAU) has the authority to catalog and name stars, and they do not sell those names, for profit or otherwise.
Now, as for why Andromeda is only visible in winter: You can only see certain constellations at certain times of the year because the Earth is orbiting around the Sun. Different parts of the sky are facing the "night" side of Earth in summer than in winter, and the light from the Sun-- what we call "daylight"-- makes it impossible to see the stars that are located behind the Sun at that time.
Basically, the Sun projects a "wall of light" which eliminates night (darkness, the natural state of the universe). At any time, the only stars we can see in "our" sky are those that are shielded from sunlight by the Earth itself. Think of the stars as being glow-in-the-dark stickers on a piece of white cardboard: if you put that cardboard out in sunlight, it's nearly impossible to see the stars, because their light is too dim compared to the sunlight. But if you stand between the Sun and the cardboard to cast a shadow (or take the cardboard into a dark room), you'll be able to see the stars, because they're then brighter than their surroundings.
Regarding the formation of new stars: Since it takes hundreds of millions of years for stars to form, it doesn't really make sense to talk about a "time of the year" when it comes to star births. Astronomical events happen over very long periods of time.
For example, dinosaurs roamed the Earth for some five hundred million years, longer than any other type of complex animal life on Earth. Our Sun is expected to "live" for about fifteen billion years. So all species of dinosaurs that ever lived, lived for less than four percent of the Sun's lifespan! (To put it in human terms: if you were the Sun and the dinosaurs were your household pets, and you were both born at the same time, they'd be dead before you began attending kindergarten.)
Also remember that the universe is a huge place, and many stellar objects are too distant or too dim or us to see from Earth. Light can only travel at about 186,000 miles per hour in vacuum, so the starlight we see from Earth is already many years old. For example, Almach, one of the stars in the constellation Andromeda, is 355 light-years away-- that means the light we're seeing from Almach now was transmitted in the year 1643 (when Oliver Cromwell was still alive)!
Some of the stars in "our" sky may not even exist any more. And right now, as you're reading this, there's probably a star being "born" somewhere in the cosmos-- we just can't see it. Mind-boggling, isn't it?
For more information on astronomy, check out these web sites:
Hope this helps!
Try the links in the MadSci Library for more information on Astronomy.