Yes, redder means the slope of the spectra favors longer-period. Both earthquakes and tremor have power at all frequencies, but tremor has relatively more at longer periods and earthquakes at higher periods. It is actually more complicated, as the spectra have kinks we call corners, so there are several regimes to consider.

"Deeper" and "at the lower edge of the seismicity" are not so different.

There are also indications that tremor can migrate up and downdip at a rate of about 50km/hr.