First of all - everything you deal with is a "chemical". You drink water? Chemical. Carrot juice? Water with chemicals. You eat an apple? Oh my, someone even prepared a list of chemicals present in an apple, it looked exactly as the list of ingredients in a Mars bar combined with water sanitizer, was just several times longer.
Second: it is dose that makes a poison. There are many substances ("chemicals" if you want) that are absolutely necessary for living but poisonous in excess. Heavy metal like zinc is an environmental hazard, yet you need traces in your body for a correct working of some of the enzymes, if memory serves me well same about manganese and copper. Excessive doses of vitamin D will make you sick and will probably kill you given time. And so on, and so on, and so on, these are obvious examples that I could list a vista, there is plenty of others. Your body deals with numerous poisons and pathogens all the time, it evolved to do so and is quite effective at keeping you alive and well despite all the risks.
Third: there is no "one size fits all" answer. All mechanisms you described can act, depending on the substance and its amount. Plus, many of the potentially harmful compounds are metabolized in the liver, which is actually why poisonings often end with liver damage.