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$(1)$ Multimeter shows deflection when it connects with capacitor
$(2)$ If we assume that $LED$ has negligiable resistance then multimeter shows no deflection for the forward blas but when it connects in reverse direction, it break down occurs so splash of light out.
$(3)$ The resistance of metal wire may be taken zero, so no deflection in multimeter
$(4)$ No matter, how we connect the resistance across multimeter It shows same deflection.