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Dawes' empirical limit for splitting double stars is 116/aperture in millimetres, giving 0.58 arcseconds for a 200 mm telescope. The theoretical Rayleigh criterion at 550 nm is slightly larger at 0.69 arcseconds. That resolution corresponds to about 1.3 km of lunar detail, and the same aperture reaches roughly magnitude 14 visually.
Dawes limit
resolution(arcsec) = 116 / aperture in mm
Rayleigh criterion
resolution = 1.22 lambda / D, converted to arcseconds
Dawes is an empirical result for equal-brightness double stars, where the eye can detect an elongated blur. Rayleigh is the formal diffraction criterion.
Usually yes. Typical seeing is 1-2 arcseconds, so apertures above about 150 mm are limited by the atmosphere rather than optics.