We present millimeter and radio observations of 13 SDSS quasars at redshifts z~6. We observed 11 of them with the Max Planck Millimeter Bolometer Array (MAMBO-2) at the IRAM 30 m telescope at 250 GHz and all of them with the Very Large Array (VLA) at 1.4 GHz. Four sources are detected by MAMBO-2 and six are detected by the VLA at the >~3 σ level. These sources, together with another six published in previous papers, yield a submillimeter/millimeter- and radio-observed SDSS quasar sample at z~6. We use this sample to investigate the far-infrared (FIR) and radio properties of optically bright quasars in the early universe. We compare this sample to lower redshift samples of quasars observed in the submillimeter and millimeter wavelengths [(sub)mm] and find that the distribution of the FIR-to-B-band optical luminosity ratio (L_FIR/L_B) is similar from z~2 to 6. We find a weak correlation between the FIR luminosity (L_FIR) and B-band optical luminosity (L_B) by including the (sub)mm observed samples at all redshifts. Some strong (sub)mm detections in the z~6 sample have radio-to-FIR ratios within the range defined by star-forming galaxies, which suggests possible coeval star-forming activity with the powerful AGN in these sources. We calculate the rest-frame radio-to-optical ratios (R^*_1.4=L_ν,1.4GHz/L_ν,4400Å) for all of the VLA-observed sources in the z~6 quasar sample. Only one radio detection in this sample, J083643.85+005453.3, has R^*_1.4~40 and can be considered radio-loud. There are no strong radio sources (R^*_1.4>=100) among these SDSS quasars at z~6. These data are consistent with, although do not set strong constraints on, a decreasing radio-loud quasar fraction with increasing redshift.