Considered is the beam wave guidance and scattering by 2D quasi-optical reflectors modeling the components of beam waveguides. The incident field is taken as the complex-source-point field to simulate a finite-width beam generated by a small-aperture source. A numerical solution is obtained from the coupled singular integral equations (SIEs) for the surface currents on reflectors, discretized by using the recently introduced Nystrom-type quadrature formulas. This analysis is applied to study what effect the edge illumination has on the performance of a chain of confocal elliptic reflectors. We also develop a semianalytical approach for shaped reflector synthesis after a prescribed near-field pattern. Here a new point is the use of auxiliary SIEs of the same type as in the scattering analysis problem, however, for the gradient of the objective function. Sample results are presented for the synthesis of a reflector-type beam splitter.