We study the interstellar medium in a sample of 27 high-redshift quasar host galaxies at z greater than or similar to 6, using the [C ii] 158 mu m emission line and the underlying dust continuum observed at similar to 1 kpc resolution with Atacama Large Millimeter Array. By performing uv-plane spectral stacking of both the high and low spatial resolution data, we investigate the spatial and velocity extent of gas and the size of the dust-emitting regions. We find that the average surface brightness profile of both the [C ii] and the dust continuum emission can be described by a steep component within a radius of 2 kpc and a shallower component with a scale length of 2 kpc, detected up to similar to 10 kpc. The surface brightness of the extended emission drops below similar to 1% of the peak at radius of similar to 5 kpc, beyond which it constitutes 10%-20% of the total measured flux density. Although the central component of the dust continuum emission is more compact than that of the [C ii] emission, the extended components have equivalent profiles. The observed extended components are consistent with those predicted by hydrodynamical simulations of galaxies with similar infrared luminosities, where the dust emission is powered by star formation. The [C ii] spectrum measured in the mean uv-plane stacked data can be described by a single Gaussian, with no observable [C ii] broad-line emission (velocities in excess of greater than or similar to 500 km s(-1)), which would be indicative of outflows. Our findings suggest that we are probing the interstellar medium and associated star formation in the quasar host galaxies up to radii of 10 kpc, whereas we find no evidence for halos or outflows.