X-ray emission from quasars has been detected up to redshift $z=7.5$, although only limited to a few objects at $z>6.5$. In this work, we present new Chandra observations of five $z>6.5$ quasars. By combining with archival Chandra observations of six additional $z>6.5$ quasars, we perform a systematic analysis on the X-ray properties of these earliest accreting supermassive black holes (SMBHs). We measure the black hole masses, bolometric luminosities ($L_{rm bol}$), Eddington ratios ($lambda_{rm Edd}$), emission line properties, and infrared luminosities ($L_{rm IR}$) of these quasars using infrared and sub-millimeter observations. Correlation analysis indicates that the X-ray bolometric correction (the factor that converts from X-ray luminosity to bolometric luminosity) decreases with increasing $L_{rm bol}$, and that the UV/optical-to-X-ray ratio, $alpha_{rm ox}$, strongly correlates with $L_{rm 2500}$, and moderately correlates with $lambda_{rm Edd}$ and blueshift of CIV emission lines. These correlations are consistent with those found in lower-$z$ quasars, indicating quasar accretion physics does not evolve with redshift. We also find that $L_{rm IR}$ does not correlate with $L_{rm 2-10 keV}$ in these luminous distant quasars, suggesting that the ratio of the SMBH growth rate and their host galaxy growth rate in these early luminous quasars are different from those of local galaxies. A joint spectral analysis of the X-ray detected $z>6.5$ quasars yields an average X-ray photon index of $ Gamma=2.32^{+0.31}_{-0.30}$, steeper than that of low-$z$ quasars. By comparing it with the $Gamma-lambda_{rm Edd}$ relation, we conclude that the steepening of $Gamma$ for quasars at $z>6.5$ is mainly driven by their higher Eddington ratios.
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