Electro-osmotic flows (EOF) have seen remarkable applications in lab-on-a-chip based microdevices owing to their lack of moving components, durability, and nondispersive nature of the flow profiles under specifically designed conditions. However, such flows may typically suffer from classical Faradaic artifacts like electrolysis of the solvent, which affects the flow rate control. Such a problem has been seen to be overcome by employing time periodic EOFs. Electric field induced transport of a conductive liquid is another nontrivial problem that requires careful study of interfacial dynamics in response to such an oscillatory flow actuation. The present study highlights the role of electric field generated Maxwell stress and free surface potential along with the electric double layer thickness and forcing frequency, toward influencing the interfacial transport and fluid flow in free-surface electro-osmosis under a periodically varying external electric field, in a semi-analytical formalism. Our results reveal interesting regimes over which the pertinent interfacial phenomena as well as bulk transport characteristics may be favorably tuned by employing time varying electrical fields.