The report presents the results of broadband dielectric spectroscopy (BDS) studies in bulk nanocolloids: E7 liquid crystalline (LC) mixture plus C60 fullerene nanoparticles. BDS spectra for 260 temperatures from the isotropic liquid (I) phase at ~360K to the nematic (N) phase at the glass temperature Tg~220K was tested. The analysis focused on pretransitional critical-like features and complex glassy dynamics, highlighting their interplay and dominance. This is associated with pretransitional fluctuations, which impact the nematic phase even 90 K below the I-N transition. On approaching Tg, strong previtreous changes detected via dielectric constant and the loss curve maximum appear, starting at Tg+30K. The critical-like behavior on T→Tg appears explicitly also for the parameter describing the distribution of relaxation times. For the 3 main relaxation times in the long-range nematic phase, the optimal portrayal via the new Critical & Activated equation is evidenced. The derivative-based test of coupling/decoupling between translational and orientational processes reveals strong decoupling with the fractional exponent F< 1 below the I-N transition and related to F< 1 above Tg. Notable is the permanent ‘parallel’ orientation of LC molecules by C60 fullerene nanoparticles, which can be significant for applications.