What does it mean to burn incense and smoke the bottom? Incense is the kind with a wooden pole at the bottom and incense at the top. I ordered four sticks, only the leftmost one was made of wood.

This incense should be of the type with a wooden core in the middle, and the wooden core runs through the whole incense. When burning, high temperature will carbonize the wood core that is about to burn, and some smoke will be generated inside the burning point. Just because there are gaps or holes formed by plant fibers in the wood core of this incense, the resistance is small, so the smoke will be generated at the bottom of the incense.

As for other meanings, don't worry, most of them belong to superstition. The Diamond Sutra says that "all appearances are illusory ..." It is not only appearances that make us persistent, but also the three generations of cause and effect mentioned by Buddhism. We should accept what we deserve, bear and repent what we deserve, strive to do altruistic things without self, and treat all sentient beings with compassion, so as to be "free from worries" and "fearless". May you be lucky and comfortable!