Do all chiral objects rotate the plane of polarization of EM waves? For example my hand is chiral, will it rotate the plane of polarization of EM waves of suitable wavelength?
Of course it will, provided you have a billion of it. (One molecule does not rotate much, after all.) Also, each should come without the rest of the body, or at least without the other hand, otherwise that would make a racemic mixture. (I'll leave the grisly details to the reader's imagination.) Also, each hand should form the same gesture, otherwise the destructive interference will ruin the effect.
Also, light of suitable wavelength would be microwave radiation, and a cursory search seems to indicate that the methods of polarizing it and measuring its polarization are known.
With all these conditions fulfilled, I don't see any difference from the situation with the molecules and ordinary light.
The wavelength has to be comparable with the object size in order to see those effects. Your macroscopic hand will not rotate ordinary light even if you have millions hands around, because the wavelength of light is so small. Yes, it will scatter light as a large object. This idea of optical rotation by long wavelengths and by large objects was shown more than 100 years ago by J.C. Bose, using twisted pieces of jute (a type of rope made from plants). Bose was in India and jute was a common material there to play around.
See this article.