  Quasars are galaxies hosting accreting supermassive black holes; due to their
brightness, they are unique probes of the early universe. To date, only few
quasars have been reported at $z > 6.5$ ($<$800 Myr after the Big Bang). In
this work, we present six additional $z \gtrsim 6.5$ quasars discovered using
the Pan-STARRS1 survey. We use a sample of 15 $z \gtrsim 6.5$ quasars to
perform a homogeneous and comprehensive analysis of this highest-redshift
quasar population. We report four main results: (1) the majority of
$z\gtrsim$6.5 quasars show large blueshifts of the broad CIV
1549\AA$\,$emission line compared to the systemic redshift of the quasars, with
a median value $\sim$3$\times$ higher than a quasar sample at $z\sim$1; (2) we
estimate the quasars' black hole masses (M$\rm_{BH}\sim$0.3$-$5 $\times$
10$^{9}$ M$_{\odot}$) via modeling of the MgII 2798\AA$\,$emission line and
rest-frame UV continuum; we find that quasars at high redshift accrete their
material (with $\langle (L_{\mathrm{bol}}/L_{\mathrm{Edd}}) \rangle = 0.39$) at
a rate comparable to a luminosity-matched sample at lower$-$redshift, albeit
with significant scatter ($0.4$ dex); (3) we recover no evolution of the
FeII/MgII abundance ratio with cosmic time; (4) we derive near zone sizes;
together with measurements for $z\sim6$ quasars from recent work, we confirm a
shallow evolution of the decreasing quasar near zone sizes with redshift.
Finally, we present new millimeter observations of the [CII] 158 $\mu$m
emission line and underlying dust continuum from NOEMA for four quasars, and
provide new accurate redshifts and [CII]/infrared luminosities estimates. The
analysis presented here shows the large range of properties of the most distant
quasars.
