The liver works with the excretory system because it filters out the toxins in your blood. The liver can be compared to a filter or a strainer. The healthy, clean blood passes to the rest of the body, and the toxins are removed. So, it excretes waste from your blood. Now, as for how the liver works with the circulatory system, it simply removes toxins in your blood so the blood can continue to do it's job and move safely throughout your body. Hope this was helpful!
There isn't anything wrong when you poop right after you eat. It's good actually. It means you have high metabolism. If you have high metabolism, you are probably skinny or average. High meatabolism means that the food you take in is absorbed quickly and that makes you feel like you have to go.