Q: If I have Chalice of the Void in play with 2 counters on it, and I play Shrapnel Blast sacrificing the Chalice of the Void, will the Shrapnel Blast resolve or be countered by the Chalice?
A: Shrapnel Blast will resolve. The Shrapnel Blast player can sacrifice his Chalice to pay for Blast without fear of it being countered because the Chalice only triggers upon complete announcement of the spell in question. The spell becomes played when all steps of announcement, ending with paying all costs, have been completed (rule 409.1i). By the time the Chalice would trigger, it's no longer in play, so there's nothing to trigger.
As for you final question, I hear reading the card is still good:
As an additional cost to play Tinker, sacrifice an artifact.
Search your library for an artifact card and put that card into play. Then shuffle your library.