For Q1: A proper weld made with the proper rod and not contaminated with another metal should not have to be ground or have any material removed. It does need to be passivated to restore the chromium. If the weld is rusting, the welder used the wrong rod (or wire) or they cleaned, brushed, ground or sanded the weld and/or welding area with something that contains ferrous metal or was contaminated by ferrous metal.
To clean it; scrub it well with a white scrubby and Bar Keepers Friend. This should remove the surface rust and repassivate the stainless. If it keeps coming back or is really deep, then the weld is contaminated and short or removing it and starting over, you'll have to keep up the BKF scrub routine.
Q2: Don't have an element and can't answer that.