If the TE's freeze due to a problem you are not going to move them any more, so I'd assume they are at the indicated stuck position and the QRH will lead you to the correct Vref for landing.
Should you lose power to the gauge, but the flaps are working, then you either trust the flaps are where you select them, (feel the trim change and the required N1% makes sense), or you select land flap very early and have the F/O on the cabin telephone looking at them. Not the best use of pilots close to landing, but..... and may be dis-allowed by security SOP's.