Do you think Varys knows anything about the coming of the Others? If he has any of his ‘birds’ at the Wall, he should know, or not?

No. Varys is entirely focused on the game of thrones. I don’t know if he’ll be alive long enough to hear that the Wall has come down and that the Army of the Dead is on the march, but that’s almost a different “Age of Man” from the one he understands and operates in.