Stump the Hardcore Lucy Fan? It Can't Be Done!

I've mentioned before that I do a daily trivia challenge on Facebook's Classic TV Lovers' Haven page. Although I try to cover a variety of shows and stars in my questions, about once a week or so I find myself asking about I Love Lucy. More than any other show included, this is the one that classic TV fans know backwards and forwards.

With 10,000 members in the group, it usually takes no more than five minutes -- often less -- for someone to correctly answer a Lucy query. These are a few I've tried recently:

1.  What's the name of the movie for which Lucy and Ethel perform a publicity stunt (seen above) atop the Empire State Building?

2.  According to Lucy Ricardo, whose personal habits include "scratching himself, and peeling bananas with his feet"?

3.  After Ricky Ricardo refuses to appear in his wife's play A Tree Grows in Havana, what does Lucy retitle her drama?

4.  What did Ricky Ricardo do after reading - and misunderstanding - Lucy's note that read "BUY CAN ALL PET"?

If you're interested enough to read this blog, I'm guessing that you won't have much trouble answering these either. But if you're stumped, drop me a note. It's always nice to hear from a fellow Lucy fanatic.