My answers

If one planet in our solar system, other than Earth, could be made to simply disappear, which would ...

• Have the most profound impact on the structure and mechanics of our system?
• Have the most profound impact on the collective imagination of mankind?
  

Jupiter for sure. Jupiter has more than twice the mass of all the other planets combined and it's stabilizing gravitational influence is probably the reason that we have a Solar System of planets in the first place. It also acts as a giant vacuum cleaner for comets (remember Shoemaker-Levy 9) that are circling the sun, thus protecting the inner planets. If it disappeared it would seriously destable the orbits of all the planets, probably causing the Earth's orbit to shift inwards towards the sun where we would all fry. Before we got pumelled by comets from the Oort cloud that surrounds the sun.

Mars - if the God of war went then there would no more wars right? :-)

What's more common in modern-day debate ...

• Premises stated, but poorly established as true, or
  
• Unstated premises, simply assumed to be true, or
  
• Poorly argued conclusions stemming from premises, or
  
• Conclusions that have no relationship to premises previously asserted?

Common - but then it's not really a debate because one side dismisses the other

Very common - then the debate rages around the assumptions being made

Most common - the debaters agree on the premises but not on what those premises lead to. This is because one party sees more than the other. This is how new scientific theories come out I guess, Einstein found a better conclusion to precession of the orbit of Mercury than Newton, based on the evidence.

Very common - tangential logic. Guilty!

What's your favorite ...

• Meal you'd confess to in the company of business professionals
• Meal you'd confess to me here
  

Beans and poached egg on toast (I'm not proud)
Beans and poached egg on toast

You really liked that chip butty didn't ya !!??

If aliens came to visit us, which would freak out mankind more ...

• Aliens that were fundamentally different from us (think "Horta" on Star Trek)?
• Aliens that were essentially just like us?
  

We'd be freaked out in general. But if they looked like spiders we'd be more freaked. If they looked like anything that is in our instinctual programming to avoid, then we'd be more scared than if not. You make a good point about if they looked like "angels". Then we'd be jealous and probably true to breed with them.

If you were instantly transformed into another living organism -- and was consciously aware with your human awareness that you were that other
organism -- which organism would you LEAST want be? Why?

A fly. They eat turds. I'd rather be an amoeba!

If you had the ability to be immortal, what aspect of immortality -- other than the "Highlander" thing with friends/family dying off -- would be most disturbing?

Boredom first, having done everything that it's possible to do on Earth. Then when the sun goes nova living inside a fireball for a few hundred million years - which would be boring (and potentially painful). Then more boredom when the Universe ends and I'd be living in darkness for ever. zzzzz.

You have a video camera and a time machine ... other than the birth of Jesus, his crucifixion or resurrection or ascension (I'm intentionally ruling out the obvious stuff), what event of history would you want to tape and bring back to modern day?

Kennedy's assasination, was it really Lee Harvey Oswald?
Unsolved murders (to help catch the crooks!)
My father meeting my mother
Einstein saying "At what time does Oxford arrive at this train?" to a train guard
The Ministry of Jesus - his time in the wilderness
The Pyramids being built
The Construction of Stonehenge
Dinosaurs
Life first forming on Earth
The Big Bang (and before)

best of all though

God creating Adam out of dust.

How would modern society be altered if that one event you taped and brought back turned out to be radically different from what people thought it was? Why

Everyone would have to believe in The Bible then, and Genesis in particular. This might make a better world.