Rise & Shine is primarily a surfactant that will work well on the leaves, and it also has some insecticidal and fungicidal properties.
It will not be good for the pots.
For cleaning mineral residues from pots, some have advised soaking them in hot water containing about a cup-per-gallon of Epsom Salts, while others state that citric acid is the way to go.
In my opinion, clay pots are not that expensive, so I get new ones.