The class of Be stars are the epitome of rapid rotators in the main sequence. These stars are privileged candidates for studying the incidence of rotation on the stellar internal structure and on non-radial pulsations. Pulsations are considered possible mechanisms to trigger mass-ejection phenomena required to build up the circumstellar disks of Be stars. Time series analyses of the light curves of 15 faint Be stars observed with the CoRoT satellite were performed to obtain the distribution of non-radial pulsation (NRP) frequencies in their power spectra at epochs with and without light outbursts and to discriminate pulsations from rotation-related photometric variations. Standard Fourier techniques were employed to analyze the CoRoT light curves. Fundamental parameters corrected for rapid-rotation effects were used to study the power spectrum as a function of the stellar location in the instability domains of the Hertzsprung-Russell (H-R) diagram. Frequencies are concentrated in separate groups as predicted for g-modes in rapid B-type rotators, except for the two stars that are outside the H-R instability domain. In five objects the variations in the power spectrum are correlated with the time-dependent outbursts characteristics. Time-frequency analysis showed that during the outbursts the amplitudes of stable main frequencies within 0.03d-1 intervals strongly change, while transients and/or frequencies of low amplitude appear separated or not separated from the stellar frequencies. The frequency patterns and activities depend on evolution phases: i) the average separations between groups of frequencies are larger in the zero-age main sequence (ZAMS) than in the terminal age main sequence (TAMS) and are the largest in the middle of the MS phase; ii) a poor frequency spectrum with f<1d-1 of low amplitude characterizes the stars beyond the TAMS; and iii) outbursts are seen in stars hotter than B4 spectral type and in the second half of the MS. The two main frequency groups are separated by {delta}f=(1.24+/-0.28).f_{rot}_ in agreement with models of prograde sectoral g-modes (m=-1,-2) of intermediate-mass rapid rotators. The changes of amplitudes of individual frequencies and the presence of transients correlated with the outburst events deserve further studies of physical conditions in the subatmospheric layers to establish the relationship between pulsations and sporadic mass-ejection events.