Wave-particle duality is the name for the fact that tiny particles of matter and energy behave like waves in some ways and like particles in others. This behavior is modeled in quantum mechanics by a mathematical construct called a wavefunction.
In quantum mechanics, wavefunction is a mathematical representation of a particle. Taking the square modulus of the wavefunction produces a probabilistic prediction about the location of a particle, but does not indicate a single definite position.
The weak force (or weak interaction) is a fundamental interaction between all particles in the standard model. The weak interaction dictates the way fundamental particles can decay into other fundamental particles (for example, the phenomenon of radioactive beta decay). The weak force is mediated by the weak bosons.