We investigate the properties of the magnetocapacitance and dissipation factor of epitaxial graphene Hall bars with different electrode configurations to gain insight into the underlying physical mechanisms. The dependence of magnetocapacitance and dissipation factor on the magnetic field shows how the screening ability of the two-dimensional electron gas (2DEG) changes at the transition from the nonquantized to the quantized state. Both magnetocapacitance and dissipation factor exhibit a characteristic and correlated voltage dependence, which is attributed to the alternating contraction and expansion of the nonscreening 2DEG regions due to the alternating local electric field. Two regimes with seemingly different voltage dependencies are explained as the limiting cases of weak and strong electric fields of the same general voltage dependence. Electric fields in the plane of the 2DEG are found to cause about three orders of magnitude more ac dissipation than perpendicular electric fields. This strong directionality is attributed to the fact that the electrons are mobile in the plane of the 2DEG but are confined in the third dimension. In the quantized state, not only the screening edge of the 2DEG but also compressible puddles embedded in the bulk cause ac dissipation, as follows from the measured frequency dependence. Finally, characteristic parameters like the width of the screening edge, the threshold voltage, and the charging time of the compressible puddles are determined. .