If someone delays making up fasts for a year, can they give fidyah before performing qada?
Yes, it is permissible to give fidyah before making up the missed fasts (qada), because each is an independent obligation, and there is no required order between them.
What is the ruling if a postpartum woman becomes pure before forty days; are acts of worship obligatory upon her, and is she permissible for her husband?
If the postpartum woman becomes definitely pure before forty days, she must perform the ritual bath and perform acts of worship as a pure woman does. What was prohibited for her also becomes permissible, so she becomes permissible for her husband after her bath. The minimum duration for postpartum bleeding is a moment (an instant), and its usual maximum is forty days. Reaching forty days is not a condition; rather, it is sufficient for the blood to stop or to see the white discharge (qassa bayda'). And Allah the Almighty 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.
What are the Sunnahs and etiquettes recommended for the person offering the Udhiyah?
In the Name of Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
There are several Sunnahs (prophetic traditions) and etiquettes that are highly recommended for the person offering an Udhiyah (sacrificial offering) to observe:
First:
It is a Sunnah for anyone intending to offer a sacrifice to refrain from cutting or removing any of their hair or nails once the first ten days of Dhul-Hijjah begin. This is based on the statement of the Prophet (peace and blessings be upon him): "When the ten days [of Dhul-Hijjah] begin and one of you intends to offer a sacrifice, let him not touch any of his hair or skin." (Narrated by Muslim)
However, if someone does happen to remove any hair or nails, they have not committed a sin, and their sacrifice remains perfectly valid.
Second:
The person offering the sacrifice should ideally slaughter the animal themselves. If they are unable to do so, they should at least witness its slaughter. This is drawn from what our Master, the Messenger of Allah (peace and blessings be upon him), said to Lady Fatima (may Allah be pleased with her):
"Stand up and witness your sacrifice, for with its very first drop of blood, every sin you have committed will be forgiven." (Narrated by Al-Tabarani in his Mu'jam, Al-Hakim in his Mustadrak, and Al-Bayhaqi in his Sunan)
Third:
Face the Qiblah (the direction of prayer) at the time of slaughtering, as the Qiblah is the most honorable of directions.
Fourth:
Pronounce the name of Allah (Tasmiyah) at the moment of slaughter by saying: "Bismillah ar-Rahman ar-Rahim" (In the Name of Allah, the Most Gracious, the Most Merciful). Even if one forgets to say it, the meat remains lawful (Halal) to eat. Allah, Blessed and Exalted is He, says:
"So eat of that [meat] upon which the name of Allah has been mentioned." (Al-An'am: 118)
It is also recommended to send blessings upon our Master, the Messenger of Allah (peace and blessings be upon him), and to follow it with the Takbeer (Allahu Akbar).
Fifth:
Supplicate for acceptance by saying: "Allahumma hadhihi minka wa ilayka, fa-taqabbal minni" (O Allah, this is a blessing from You and is offered back to You, so please accept it from me). This means: This sacrifice is a blessing that originated from You, and I am offering it to draw closer to You. And Allah the Almighty Knows Best.