Is an 'Urfi marriage without witnesses invalid, and is a woman required to observe 'iddah after a divorce from it?

According to the majority of jurists, marriage is not valid except with a guardian (wali) and two witnesses. The marriage contract is void if it is concluded without them. If a woman marries without a guardian or witnesses, she is not permitted to marry another man until separation occurs between them and her iddah (definition) (waiting period) expires. The husband must divorce her, and if he refuses, the ruler (qadi) shall annul the marriage and separate them. A woman who has been intercoursed in a dubious union or an invalid marriage must observe the iddah of a divorced woman (three menstrual cycles, or three months for a post-menopausal woman, or upon giving birth for a pregnant woman).