Question: Except for "Come on, Eileen", what other songs were Tommy and Richard singing to while driving?
Answer: In that scene, that song is followed first by "It's the End of the World as we Know It (And I Feel Fine) " (R.E.M.) and then by "Eres tú" (Mocedades). Earlier, they sing "Superstar" (The Carpenters) just before the hood flies off.
Answer: A number of online explanations said it was because Lowe was already contractually tied to another project while this one was being filmed. Another explanation is that he was left uncredited so his appearance mid-film would come as a "surprise" when the plot took a different turn.
I read where his contract with the mini-series "The Stand" left him unable to take any credited roles. However, it seems "Tommy Boy" began filming after "The Stand" aired and he was credited for his role as Jesse James in "Frank and Jesse." However, it seems to be an Internet story where the source isn't credited.
Answer: It's a bit of movie silliness, mostly. She'd definitely have been arrested in real life. If you wanted to justify it, you could say that Paul was the one who actually did all the illegal acts (bigamy aside), so he was the one the police would be most interested in apprehending. Beverly could still be arrested at a later date if Paul provided evidence of her involvement in the various crimes they committed (her bigamous marriage would definitely constitute a felony since it was done to defraud the Callahans).