Frank Harte sings it way he does to immitate the sound of the old Dublin Street sellers who would have used that sort of sing song lilt to advertise their goods, which is presumably what Molly would have been doing, although there's some that say she sold other things as well. Her Dublin statue has been christened the Tart with the Cart by local wits. As to the other points she definitely Wheeled her wheelbarrow and she died of a faver (local pronunciation).

I'm singing the song in a ballad group competition tomorrow, although it wouldn't have been my choice.