If Haldir and the elves went to Minas Tirith instead
 

If Elrond sent Haldir and the elves with Aragorn to take the Corsairs ships together with the dead army, would that have worked? Could the Helms Deep battle still be spectacular without the elves coming to their aid?

Sure. It was quite spectacular in the book, with Legolas the only Elf present.

And also in the book, the sons of Elrond and Rangers of the North went with Aragorn through the Paths of the Dead/etc.

Are we talking book or movies? If movies, then Haldir and his company were all dead. If books, they don't exist (Haldir does, as a marchwarden of Lorien, but has nothing to do with Elrond).