In a generic setup, where metasurface is placed between the two antennas, what should be the minimum distance between the two antennas for accurate measurements: preferably in far field.?
The far-field distance depends on the horn dimensions and the frequency of operation. It must be greater than L = (2*D^2)/lambda, where D is the largest dimension of the horn aperture and lambda is the wavelength at the frequency you are testing at. If you want the metasurface to operate in the far-field of each antenna then the distance between the two horn antennas should be >2*L (i.e. distance between the metasurface in the middle and each horn is > L).
If you want to reduce the far field distance, which will be quite large if the resonance occurs at low frequency and the illuminating horn has a wide aperture too! then try thinking of designing patches instead of horn although a bit of gain compromise has to be kept in mind!
Yes, a large aperture is indeed a problem. You are suggesting to use patch antennas instead. However, will patch antennas be sufficient for measurement of metasurfaces. Is there any literature that you can refer in this regard.