The more electropositive element should displace metal from it's salts' solution. This can be seen in reaction of copper salts with iron. But, if you try using for example potassium metal as the more electropositive metal in a displacement reaction you don't get a result since potassium will react with water before it has a chance to displace much of the other metal.
What makes dissolution in water favour displacement by the more electropositive metal, even if calculated gibbs free energy for the reaction would be positive? Is it the higher strength of hydrogen bonding of the more electropositive metal, or is it the lack of lattice energy of the salt that otherwise needs to be overcome?
This will depend on the answer to the first question, but is it possible to actually displace, say, Calcium with Potassium metal from any of it's salts provided that this salt is soluble and the solvent is inert towards Calcium and Potassium metal? If you had to do this in reality, what would you use, perhaps a phase transfer catalyst?
I imagine that if it's mainly the lattice energy making the difference one should be able to just use a different solvent, as it would be only important to dissociate the salt