Relationship between sensors and materials in terms of electromagnetic spectrum
But the wavelength of electromagnetic wave required to “see” an object must be same size or smaller than the object.


Essentially, the waves are unaffected (at least not enough to be detected) by objects that are smaller than the wavelength. Since we look at the distortion in the waveform to image objects, no distortion would mean an object is undetectable.

Imagine you are walking down a rocky path. Small rocks and pebbles would not change your gait at all, so they would be undetectable to you. Large stones, however, would force you to change your step, making them detectable. If you were much smaller and took shorter steps (or a shorter wavelength), then these small objects would become detectable to you.

So, to answer your questions:


  For the water molecule example, why do the authors refer to a source
  emitting ?


Because it is the wavelength of the radiation source which matters for imaging.


  Therefore, to image water molecules, a source which emits far
  ultraviolet/soft X-rays is needed. Passing this through water would
  somehow let us image water molecules. Is that what they mean ?


At that wavelength or smaller, yes. Operating at that wavelength, with the proper detection equipment, should allow you to image water molecules and larger.