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The power absorption dynamics of electrons and the electrical asymmetry effect in capacitive radio-frequency plasmas operated in CF4 and driven by tailored voltage waveforms are investigated experimentally in combination with kinetic simulations. The driving voltage waveforms are generated as a superposition of multiple consecutive harmonics of the fundamental frequency of 13.56 MHz. Peaks/valleys and sawtooth waveforms are used to study the effects of amplitude and slope asymmetries of the driving voltage waveform on the electron dynamics and the generation of a DC self-bias in an electronegative plasma at different pressures. Compared to electropositive discharges, we observe strongly different effects and unique power absorption dynamics. At high pressures and high electronegativities, the discharge is found to operate in the drift-ambipolar (DA) heating mode. A dominant excitation/ionization maximum is observed during sheath collapse at the edge of the sheath which collapses fastest. High negative-ion densities are observed inside this sheath region, while electrons are confined for part of the RF period in a potential well formed by the ambipolar electric field at this sheath edge and the collapsed (floating potential) sheath at the electrode. For specific driving voltage waveforms, the plasma becomes divided spatially into two different halves of strongly different electronegativity. This asymmetry can be reversed electrically by inverting the driving waveform. For sawtooth waveforms, the discharge asymmetry and the sign of the DC self-bias are found to reverse as the pressure is increased, due to a transition of the electron heating mode from the α-mode to the DA-mode. These effects are interpreted with the aid of the simulation results.