How do we determine solubilities?
How else but by experiment?
All of our solubility rules derive from experiment. Someone in the past or the next past century has tested the solubility of halides, of sulfates, of nitrates, etc. and noted the results. With regard to covalent compounds, again experiment is the key.
Alcohols tend to be soluble in water. Hydrogen halides (actually covalent compounds) dissolve in water with ionization. With respect to the question as to whether the solute was an electrolyte, just what is an electrolyte? How would you test this property?