Does the intention (niyyah) of the principal (muwakkil) suffice for the sacrifice (dhabḥ) of the udhiyyah?
Praise be to Allah, and peace and blessings upon our master, the Messenger of Allah.
If a person appoints an agent (wakīl) to perform the slaughter (dhabḥ) on their behalf, the intention (niyyah) of the principal (the one appointing the agent) suffices, and there is no need for the agent to have this intention himself. In fact, even if the agent is unaware that he is performing the sacrifice on someone's behalf as an udhiyyah (sacrificial offering), this does not affect its validity. And Allah, the Most High, 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.
Does using a respiratory device (oxygen) affect the validity of fasting?
Using an oxygen device does not affect the validity of fasting because oxygen is a gas with no physical substance.
However, if medicinal substances with physical particles are added to the oxygen, its use would break the fast, as it enters the body cavity through a natural passage.
A person who has recently embraced Islam is afraid of undergoing circumcision (khitān) — what should he do?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
If this person would be harmed by undergoing circumcision, based on the assessment of a trustworthy physician, then he is not obligated to undergo it. However, if the matter is simply a fear of the procedure itself, then it may be postponed until he feels at ease and settled about it, provided this does not lead him to become averse to Islam — while still taking care to remove any impurity from the concealed area [beneath the foreskin]. And Allah, the Exalted, knows best.