Hello Sameer
To answer to your question you need an entire course on numerical methods
very briefly:
1- velocity diffusivity: the value of viscosity-like coeficient that is linked to the elliptic part of the equation (Lapalcian). Its role is the introductionof diffusion.
2- advection, is the transport part, left side part of the shallow water equations
3- solver accuracy: htreshold below which the solver stops iterating
kind regards
Riadh