Yes, a liquid can diffuse through a solid, if the solid is porous, or if the solid is soluble in the liquid in question.
Yes
Opals are an example of water diffusing into rock under enormous pressure and millions of years.
Solids become liquids when the temperature reaches melting point, groups of particles start to brake away from each other. This is when the solid starts becoming a liquid. Liquids become solids on...
These are called Phase Transitions.