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We theoretically and numerically investigate the scattering behavior of a periodic parity-time (PT)-symmetric waveguide network composed of a finite number of unit cells. Specifically, we put forward rigorous and formally exact expressions for wave propagation, bi-directional reflectionless, and coherent perfect absorption and lasing (CPAL) occuring in a finite periodic optical waveguide network. Through the use of the generalized parametric space derived from observation of PT-symmetric transfer matrix, Lorentz reciprocity theorem and non-imaginary Bloch phase, we observe that when the unit cell is operated at the PT broken phase or exceptional point, the system can always have propagating modes, independent of the number and transmission phase of the unit cell. On the other hand, when the unit cell is operated at the exact PT-symmetric phase, the formation of propagating waves would depend on the transmission phase of the unit cell. More interestingly, we find that even though the unit cell is not operated at the exceptional point, reflectionless with bi-directionality as well as unity transmittance can be achieved by choosing appropriate number of unite cells and specific PT phases. We also find two approaches to implement CPAL. One is to exploit odd number of the unit cell operated at the CPAL point. Another way is to manipulate specific broken phase with an appropriate number of the unit cells, while making transmission phase to be null. We believe this work may offer a theoretical underpinnings for studying extraordinary wave phenomena of PT-symmetric photonics and may open avenues for manipulation of light.