  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 ($\langle{\rm log} (L_{\rm Bol}/L_{\rm Edd})\rangle=
-0.4\pm0.2$), 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 $z\sim6$ and $2\leq
z\leq4.5$, 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.
