Does the warranty on my work if i run over a screw a shop cant repair due to nature of hole, tires are recently purchased as of last week?

Yea 2 year road hazard, its covered, bring in the damaged tire and they will replace it

You're better off buying your tires from a reputable dealer.

I just had a similar issues, it should be covered. You have to have the tire removed from the rim, then return it to tirerack to let them inspect it. If approved, they will send a refund check for the tire.