This is actually two separate questions. Be sure you read both
answers. "What will happen when the Earth passes through the
galactic equator?" The Sun orbits the center of the Milky Way
galaxy in about 200-250 million years. However, the Sun's movement
is not a simple ellipse; it's more complicated than that and it
bobs up and down as it moves. It oscillates around 2.7 times for
every orbit, and some scientists think that the periods when it is
moving through the denser regions of the galactic plane coincide
with mass extinction events on Earth. "What does 2012 have to do
with this?" Absolutely nothing. The 2012 scare is a hoax/myth/scam.
The Sun is not currently particularly close to the galactic equator
and it won't be significantly closer in 2012.