We report the results of near-infrared spectroscopic observations of 37 quasars in the redshift range 6.3<z<=7.64, including 32 quasars at z>6.5, forming the largest quasar near-infrared spectral sample at this redshift. The spectra, taken with Keck, Gemini, VLT, and Magellan, allow investigations of central black hole mass and quasar rest-frame ultraviolet spectral properties. The black hole masses derived from the MgII emission lines are in the range (0.3-3.6)x10^9^M_{sun}_, which requires massive seed black holes with masses >=10^3^-10^4^M_{sun}_, assuming Eddington accretion since z=30. The Eddington ratio distribution peaks at {lambda}_Edd_~0.8 and has a mean of 1.08, suggesting high accretion rates for these quasars. The CIV-MgII emission-line velocity differences in our sample show an increase of CIV blueshift toward higher redshift, but the evolutionary trend observed from this sample is weaker than the previous results from smaller samples at similar redshift. The FeII/MgII flux ratios derived for these quasars up to z=7.6, compared with previous measurements at different redshifts, do not show any evidence of strong redshift evolution, suggesting metal-enriched environments in these quasars. Using this quasar sample, we create a quasar composite spectrum for z>6.5 quasars and find no significant redshift evolution of quasar broad emission lines and continuum slope, except for a blueshift of the CIV line. Our sample yields a strong broad absorption line quasar fraction of ~24%, higher than the fractions in lower-redshift quasar samples, although this could be affected by small sample statistics and selection effects.