Is it permissible to offer an absentee funeral prayer?
Yes, it is permissible to offer an absentee funeral prayer.
How does one with a continuous condition (like urinary incontinence or non-menstrual vaginal bleeding - mustahada) perform ablution?
A person with a continuous condition must do three things:
1. Not perform ablution except after the prayer time has entered.
2. Change the bag or diaper placed to reduce the flow of urine or blood after the prayer time enters, wash the private part from blood or urine, and perform ablution immediately.
3. Perform the actions of ablution in immediate succession, then pray immediately without delay, unless he intends to pray with the congregation.
It is not permissible for a person with a continuous condition to combine two obligatory prayers with one ablution, as he must perform ablution for each obligatory prayer, even if making it up (qada'). And Allah the Almighty knows best.
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.
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.