Do astronomers and astrophysicists more often use diameters or radii when discussing about planets, dwarf planets, exoplanets and stars?

Definitely radii, with one notable exception...

When observers talk about how large an object is on the sky, they usually discuss angular size, which is related to the diameter of an object, not the radius. So when discussing the angular size of, say, Alpha Centauri A (a few milliarcseconds), this is related to the diameter of the star, not the radius.