Behavior Tree (BT) planning is crucial for autonomous robot behavior control, yet its application in complex scenarios is hampered by long planning times. Pruning and heuristics are common techniques to accelerate planning, but it is difficult to design general pruning strategies and heuristic functions for BT planning problems. This paper proposes improving BT planning efficiency for everyday service robots leveraging commonsense reasoning provided by Large Language Models (LLMs), leading to model-free pre-planning action space pruning and heuristic generation. This approach takes advantage of the modularity and interpretability of BT nodes, represented by predicate logic, to enable LLMs to predict the task-relevant action predicates and objects, and even the optimal path, without an explicit action model. We propose the Heuristic Optimal Behavior Tree Expansion Algorithm (HOBTEA) with two heuristic variants and provide a formal comparison and discussion of their efficiency and optimality. We introduce a learnable and transferable commonsense library to enhance the LLM's reasoning performance without fine-tuning. The action space expansion based on the commonsense library can further increase the success rate of planning. Experiments show the theoretical bounds of commonsense pruning and heuristic, and demonstrate the actual performance of LLM learning and reasoning with the commonsense library. Results in four datasets showcase the practical effectiveness of our approach in everyday service robot applications.