Building-integrated photobioreactors (PBRs) offer a pathway for carbon-neutral architecture, yet deployment is hindered by configuration complexity and biological maintenance. This paper presents a modular PBR facade system powered by a computational framework reconciling design intent with physical validity. We introduce 'carbon-neutralization bricks' featuring integrated vessel-and-conduit geometry; monolithic fluid channels enable 'plug-and-play' assembly. To navigate the combinatorial complexity of 14 modular geometries, we develop a Computational Sketch-to-Layout Agent that formulates layout synthesis as a Constraint Satisfaction Problem (CSP). Using the CP-SAT engine, the agent treats sparse user sketches as soft priors while enforcing hard constraints like port alignment and global connectivity. This allows non-experts to synthesize fabrication-ready configurations in near real-time. Furthermore, to facilitate autonomous maintenance, we propose a weakly supervised algae health monitoring pipeline. By employing a hybrid CNN-attention backbone and a temporal ranking loss, the system quantifies biological vitality from photographs without absolute ground-truth labels. Experiments demonstrate the CSP solver achieves a 95.5% success rate on grid scales up to 15 x 15. Qualitative evaluations confirm the framework preserves design semantics while ensuring operational integrity. Long-term tests show the vision module produces health trajectories aligned with 14-day biological cycles, suggesting that integrating interactive synthesis with low-cost computer vision can democratize scalable carbon capture systems.