Wilson: (screaming at John) Who is it?
J: Who's on first, what's on second...I don't know. I can't see 'em!
Who's on first is a famous sketch by comedians Abbott and Costello. Listen to the routine here.

J: Aeryn, pick it up. I wanna get out of this rain. This is the place.
A: Rain, is that what you call this? I like it.
"Pick it up" is short for "pick up the pace" meaning "walk faster" in this context.
A little comment about how much I love that Aeryn instinctively does what we all did as kids, open our mouths and catch rain on our tongues. Of course with all the pollution, I wouldn't recommend doing so, but it's fun to see Aeryn's child-like curiosity and exuberance about a new experience.

J: It's beer...alcohol. Trust me, it's just what we need right now. Down the hatch.
A: (slowly as if not sure what she's saying) Down the hatch.
"Down the hatch" is an informal expression sometimes used when drinking a toast. Comparable phrases would be "cheers," "salud," or "sante."