For this part you would make sure that you have the box checked in your shipping tab of your eCart object for the 'include shipping in cart subtotal when calculating sales tax'. This would ensure that the shipping is included as part of the subtotal, then tax will be applied to this.
How you ensure that non NY residents are not charged tax on the shipping is in the charge rule for the tax, instead of making the calculation based on the subtotal of the cart you do it for the subtotal of the total price column, this way the shipping will not be included.