The EPR "paradox" is not a paradox (it was once mistaken for one, but is merely an example of the quantum world being unintuitive). Thus it does not really need "resolution", nor does MWI really resolve it (it is a model which is compatible with it, like all the other valid interpretations).
Schroedinger's cat is now recognised as a somewhat flawed thought experiment. The cat needs to be cooled to extremely close to absolute zero for quantum superposition to occur, when it is stone dead in all cases!
The many-worlds interpretation implies that there are very—perhaps infinitely[11]—many universes. It is one of many multiverse hypotheses in physics and philosophy. MWI views time as a many-branched tree, wherein every possible quantum outcome is realised. This is intended to resolve some paradoxesof quantum theory, such as the EPR paradox[5]:462[2]:118 and Schrödinger's cat,[1] since every possible outcome of a quantum event exists in its own universe. Wiki