Detoxing
To answer your questions, one needs to cover several issues.
A herb to promote liver health is Milk Thistle, also called St Marys thistle, botanically known as Silybum Marianum. This is ideal for such things as chirrosis of the liver (as occurs with alcoholics), and liver damage due to consuming poison. This herb has saved many lives.
In our bodies, blood flows from the heart, to various parts of the body, back to the heart, to the lungs, back to the heart, and back to the various parts of the body, and so on.
There is one exception to this. Blood flows from the heart to the intestines. From the intestines, it does not flow straight back to the heart. Instead, it flows through the liver, then back to the heart.
If a person consumes poison, the liver breaks it down. The liver may be damaged in the process. The liver is sacrificed to save the health or life of the person. Unless the liver is so severely damaged that the person dies from liver failure. Anyone in that situation, should be using Silybum Marianum.
Bitter herbs stimulate the appetite, and the secretion of acid in the stomach. Likewise, they can stimulate the flow of bile.
I will try to explain it like this: If it is nearly lunch time, and someone calls out that lunch is ready, the secretion of saliva in your mouth starts, even before you get to the table. You don't try to make it happen. It just happens.
In a similar way, bitter herbs can stimulate things. The bitter taste can cause a reaction in the autonomic nervous system, which stimulates things. The body is complex.
Many years ago they did horrible experiments on animals. For example, they got a dog, surgically modified the dog so when it ate, the food fell out through a hole in its neck. They found doing that, the dog would have increased acid in its stomach, even with no food entering it. They learnt how everything works by horrible experiments like that. The autonomic nervous system does a lot of things.
When a person is detoxifying, it is important that the bowel is efficiently eliminating toxins. If everything else is working properly, but the bowel is not, detoxifying will not be very effective.
While the liver breaks down poisons, some toxins just need to be eliminated through the bowel, not broken down.
One way to get toxins out of fat, is to eliminate the fat. That is one reason why people do fasts, or even weight loss diets. These toxins need to be eliminated through the bowel.
Historically, there was a classification of herbs called alterative herbs. These promote elimination of toxins from body tissues. One example is red clover. Used with an effective detoxification program, alterative herbs are an essential part of using natural methods to eliminate cancer.