We present the analysis of optical and near-infrared spectra of the only four z > 6.5 quasars known to date, discovered in the UKIDSS-LAS and VISTA-VIKING surveys. Our data set consists of new Very Large Telescope/X-Shooter and Magellan/FIRE observations. These are the best optical/NIR spectroscopic data that are likely to be obtained for the z > 6.5 sample using current 6-10 m facilities. We estimate the black hole (BH) mass, the Eddington ratio, and the Si IV/C IV, C III]/C IV, and Fe II/Mg II emission-line flux ratios. We perform spectral modeling using a procedure that allows us to derive a probability distribution for the continuum components and to obtain the quasar properties weighted upon the underlying distribution of continuum models. The z > 6.5 quasars show the same emission properties as their counterparts at lower redshifts. The z > 6.5 quasars host BHs with masses of 109 M that are accreting close to the Eddington luminosity (〈log(L Bol/L Edd)〉 = -0.4 ± 0.2), in agreement with what has been observed for a sample of 4.0 < z < 6.5 quasars. By comparing the Si IV/C IV and C III]/C IV flux ratios with the results obtained from luminosity-matched samples at z 6 and 2 ≤ z ≤ 4.5, we find no evidence of evolution of the line ratios with cosmic time. We compare the measured Fe II/Mg II flux ratios with those obtained for a sample of 4.0 < z < 6.4 sources. The two samples are analyzed using a consistent procedure. There is no evidence that the Fe II/Mg II flux ratio evolves between z = 7 and z = 4. Under the assumption that the Fe II/Mg II traces the Fe/Mg abundance ratio, this implies the presence of major episodes of chemical enrichment in the quasar hosts in the first 0.8 Gyr after the Big Bang. © 2014. The American Astronomical Society. All rights reserved.