Sorry, I only defined the first part. Air Yards is yards passing minus YAC.
Minus needs is taking distance for a first down (possibly distance to score near goal line-but unsure as I haven't read all the details) and subtracting it from the throw. And yes, this is only third down.
I am not sure it tells you much about Rodgers versus Manning, but it does tell you that Alex Smith is very trusting of his receivers to get YAC for a first.