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 VLT/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 mass, the Eddington ratio, and the SiIV/CIV, CIII]/CIV, and FeII/MgII 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 black holes with masses of $sim 10^9$ M$_{odot}$ that are accreting close to the Eddington luminosity ($langle{rm log} (L_{rm Bol}/L_{rm Edd})rangle= -0.4pm0.2$), in agreement with what has been observed for a sample of $4.0<z<6.5$ quasars. By comparing the SiIV/CIV and CIII]/CIV flux ratios with the results obtained from luminosity-matched samples at $zsim6$ and $2leq zleq4.5$, we find no evidence of evolution of the line ratios with cosmic time. We compare the measured FeII/MgII 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 FeII/MgII flux ratio evolves between $z=7$ and $z=4$. Under the assumption that the FeII/MgII traces the Fe/Mg abundance ratio, this implies the presence of major episodes of chemical enrichment in the quasar hosts in the first $sim0.8$ Gyr after the Big Bang.
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