Is there such a thing as a “Galactic Season”?

Answer 1

I haven't heard this term used before, but a natural understanding of it tells us, yes. Perhaps you are refering to "Galactic Oscillations".

Our orbit around the center of the Milky Way appears to oscillate in the plane of the disc. The oscillation is small with respect to the size of the galaxy, and it takes a very long time for an oscillation to happen. (on the order of millions of years)

'Weather' changes such as increases in meterorites that collide with the planet are possible, but I'm not aware of any solid evidence for this.

Answer 2

Yes.