What is the ruling on undoing braids of hair during the ritual bath?
It is not a condition to undo braids if the water reaches all the hair and penetrates to its base. If the water does not reach except by undoing the braids, then it is obligatory to undo them for the water to reach. And Allah the Almighty knows best.
What is the ruling of Islamic Law on wudu (ablution) when there is an adhesive substance on the hand that is difficult to remove?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
The general principle is: if what is applied to the limbs of wudu' (ablution) does not form a barrier substance preventing water from reaching the skin, then the wudu' is valid despite its presence. However, if these substances prevent water from reaching the skin, the wudu' is not valid with their presence, and they must be removed so that water reaches the hair or skin without any barrier.
Shaykh al-Islam, the Imam an-Nawawi, may Allah have mercy on him, says: "If there is wax, dough, henna, or similar substances on some of his limbs [of wudu'], and this prevents water from reaching any part of the limb, then his purification (tahara) is not valid — regardless of whether the amount is much or little. But if there remains on the hand or elsewhere only the trace and color of the henna, without its substance [i.e., the physical residue itself], or the trace of a liquid oil such that the water touches the skin of the limb and flows over it, though it does not remain [as a barrier] — then his purification is valid." [Al-Majmu' , Vol.1/P.529]. And Allah, the Exalted, knows best.
What is the ruling on water present on the floor of a toilet/bathroom?
The default ruling is the purity of this water present on the bathroom floor. If one is certain or strongly suspects its impurity, then one washes whatever part of the body or clothing this impure water has touched. If one doubts its impurity, the default is purity, and we do not rule it impure based on mere doubt. And Allah the Almighty knows best.
Is the marriage, which lacks a valid legal contract, a guardian, and a court registration, valid?
It is incumbent that a valid marriage contract be concluded in the presence of a guardian and two trustful witnesses, and it should be registered in the court to protect the rights of the wife. Actually, a valid marriage contract is what differentiates between sound marriage and fornication.