At my poe i have shown my visa and my latest approved extension copy which has a start date 2 months from now , but cbp officer did not give me admission based on that instead provided until current h1b petition end date . I checked with attorney and he auggested me to cross border at mexico and get i94 extended . Can that be done at laredo border ?
Yes, this is doable.
Yes, ideally you should apply for H4 extension of status with you H1b.