Is it valid to perform the obligatory prayer while sitting?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Standing (Al-Qiyam) while having the ability to do so is one of the pillars (Arkan) of the prayer; the obligatory (Faridah) prayer is not valid without it. However, whoever is unable to stand may pray sitting down. As for voluntary (Nafilah) prayers, it is permissible to pray them sitting even if one is able to stand, but the one sitting receives half the reward of the one who prays standing. And Allah the Exalted knows best.
Does nosebleed during the day in Ramadan affect the validity of fasting?
A nosebleed does not affect the validity of fasting unless some of the blood reaches the body cavity or the person intentionally swallows it. In such a case, their fast is invalid, and they must refrain from eating and drinking for the rest of the day and make up for that day later.
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.
What is the ruling of Islamic Law on eating or drinking forgetfully while observing the kaffarah fasting?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
If someone eats or drinks out of forgetfulness while fasting, it is simply that Allah has fed them and given them drink. Their fast is not broken by this; rather, they should continue fasting. This ruling applies whether the fast is an obligatory one (like Ramadan), a make-up fast (Qada), an expiation (Kaffarah), or a voluntary (Nafal) fast. And Allah the Exalted knows best.