Are all deliquescent salts highly soluble?
As already pointed out, dissolution and deliquesence are different phenomenon. 

For dissolution to take place, the energy produced by hydration of the salt's constituent ions should compensate for the energy required to break the crystal lattice. 

Solubility then depends on temperature, pH and also the amount of salt already present in the solution. (Recall: definitions of solubility products)

Hygroscopic characteristics in general can be attributed to the both absorption and adsorption (at the surface). 

Particularly, deliquescence occurs when the vapour pressure of the saturated aqueous solution of a substance is less than the vapour pressure of water in the ambient air. 

When water vapour is collected by the pure solid compound, a mixture of the solid and liquid or an aqueous solution of the compound forms until the substance is dissolved and is in equilibrium with its environment; when this happens, the vapour pressure of water over the aqueous solution will equal the partial pressure of water in the atmosphere in contact with it. 

A crystalline salt aerosol particle will deliquesce in the atmosphere when the relative humidity surpasses a characteristic value, i.e deliquescence point.