Why would Mr. Burns owe Smithers two cokes?

Because Homer was still alive after they put his brain back in his body in Treehouse of Horror II, and because everyone died in The Shinning...

Anyhow,

What franchise chain was little Miss Springfield opening when she was struck by lightening?

almost 2 weeks without a response! C'mon people!

What is the name of Bart's Siamese twin?

Hugo

What does Hibbert say in response to Lisa's objection that Siamese twins prefer to be called 'conjoined twins?'

"Hillbillies prefer to be called sons of the soil but that ain't gonna happen either."

It was on tonight for me, else I would have had no chance (and no question.)

Homer names one of the opossum living in the monorail. What does he name it, and how does he tell it from the others?

He calls the big one Bitey.

Name at least two of the Twirl Kings yo-yo performance group.

Sparkle, Cobra, Zero Gravity...

What did Burn's father do with the young soothsayer who predicted the Union movement's history instead of listening to him?

Had him bricked up or buried on concrete or something?

Old Burns: 'You there! Turn out those pockets.'

Boy does so.

Old Burns: 'Just as I thought atoms, one, two, three, SIX OF THEM... Take him away'

Boy: 'You can't do this, one day we'll form a Union and get the fair and equitable treatment we deserve! And then we'll go too far and become lazy and shiftless and the Japanese will eat us alive!'

Old Burns: 'The Japanese? Those sandal clad goldfish tenders? Bah hockletosh!'

Cuts back to Modern Burns: 'If only we'd listen to that boy instead of bricking him up in the abandoned coke oven.'

One of the greatest scenes ever.

Your question.

Hooray! Total stab in the dark.

What are the two things Mrs. Burns can do?

Dial and yell (That improvident lackwit! :p ).

Who directed "Nazi Supermen are our Superiors"?

Roger Meiers Senior.

'Roger Meiers Senior was loved by all, except during the release of his controversial 1939 film 'Nazi Supermen are our Superiors'...

Brilliant.

What's Quimby's excuse for using public treasury money to fund the murder of his enemies?

"I'm a bad widdle boy." :)

How much is the cash prize for the Montgomery Burns Awards for Outstanding Achievement in the Field of Excellence?

Two thousand dollars...

Also you get a ham and a trophy, presented by Smokinnnnnnnn Joe Frasierrrrrrrrrrr!

Who killed Snowball 1?