No she didn't. See the related link below for the soundtrack.
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A couple-This time, I'll find you, and Moondance
It was played in Rush Hour.
Mariah Carey - Fantasy
Yes he did.
Yes, in 1976, Cheap Trick opened for Rush at a concert in Rockford IL. Cheap Trick never actually toured with Rush, but they did play a couple of other gigs as Rush's opening act.