Is the circulation of water all over the body achieved merely by rinsing shampoo off the hair and body, or does it require an additional washing to circulate water after shampoo? And is the European toilet considered pure if some of its contents splash onto the thighs when relieving oneself?

If the ritual bath (ghusl (definition)) is performed with pure water after using shampoo and soap, and you ensure that all parts of your body and hair are covered with the intention of removing ritual impurity, then your ghusl is valid. The alteration of water by soap and shampoo after it reaches the body does not invalidate it, as the Hanbalis have explicitly stated that the change in water due to what is on the limb does not prevent ritual purification, because it is a change within the place of purification. However, if the pure water does not cover the entire body, then the ghusl is not complete.