The chord stuff is all perfectly reasonable (in pop music, that is; in a classical piece in the key of C you would have an Em going to an Am way more than to F, for example, and you'd see way more D chords).
I don't buy that Eb/Cm is the third most common key in pop music, though. There's not a whole lot of pop music in minor keys, and Eb is a weird key to play guitar in.
> There's not a whole lot of pop music in minor keys
In my informal survey of the first 6 songs I got on the "pop" channel on pandora, fully a third were in minor keys. (Rumor has it by Adele, and I wanna go by Britney Spears)
I think one of the primary issues with popular music is that it's often ambiguous whether it's in a major or minor mode, even when the song starts on a minor chord. Classically, one would mark the transition to a minor mode by the existence of an authentic cadence: V/vi -> vi, or by the raised scale degree 5, but neither of those clues exist in either song that you mentioned.
In songs like My Heart Will Go On, it appears that the verse tonicizes I, where as the chorus centers around the relative minor. However does it make sense to say it switches modes every time the section changes? Maybe not
I don't buy that Eb/Cm is the third most common key in pop music, though. There's not a whole lot of pop music in minor keys, and Eb is a weird key to play guitar in.