Is vomit among the nullifiers of Wudu (ablution)?
Vomit does not nullify Wudu, but it is a Najaasah (impurity) that requires rinsing the mouth and washing whatever became dirty by it since the prayer becomes valid only after the removal of Najaasah. And Allah Knows Best.
Is it permissible to slaughter one animal as a sacrifice and an Aqeeqah (the sheep slaughtered on the seventh day from the child`s birth)?
It is impermissible to do so since each of them is slaughtered for a different reason.
What does "All the deeds of the son of Adam are for him, except fasting" mean?
The Prophet ﷺ said: "Allah, the Almighty, said: 'Every deed of the son of Adam is for him, except for fasting; it is for Me, and I shall reward for it." [Agreed upon]
This means:
● Every deed of the son of Adam may be affected by showing off (riyaa’), except fasting, because only Allah knows whether a person is truly fasting or not.
● The reward for all deeds is known—one good deed is multiplied tenfold—except fasting, as only Allah knows its true reward.
Is prayer nullified by nose bleed?
All praise be to Allah, The Lord of The Worlds. Blood coming out of the nose, or a wound doesn`t nullify prayer regardless of its quantity. And Allah Knows Best.