The interplay of electron-electron interaction and confining potential can lead to the reconstruction of fractional quantum Hall edges. We have performed exact diagonalization studies on microscopic models of fractional quantum Hall liquids, in finite-size systems with disk geometry, and found numerical evidence of edge reconstruction under rather general conditions. In the present work we have taken into account effects such as layer thickness and Landau-level mixing, which are found to be of quantitative importance in edge physics. Due to edge reconstruction, additional nonchiral edge modes arise for both incompressible and compressible states. These additional modes couple to electromagnetic fields and thus can be detected in microwave conductivity measurements. They are also expected to affect the exponent of electron Green's function, which has been measured in tunneling experiments. We have studied in this work the electric dipole spectral function that is directly related to the microwave conductivity measurement. Our results are consistent with the enhanced microwave conductivity observed in experiments performed on samples with an array of antidots at low temperatures, and its suppression at higher temperatures. We also discuss the effects of the edge reconstruction on the single-electron spectral function at the edge.