Who is responsible for performing the aqiqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
The one upon whom the 'aqīqah is incumbent is whoever is obligated to financially maintain the newborn — whether the father, paternal grandfather, or mother. It is to be performed from their own wealth, not from the wealth of the newborn child.
As for one upon whom the financial maintenance of the newborn is not obligatory, they may not perform the 'aqīqah except with the permission of the one upon whom it is obligatory — namely, the father. And Allah Almighty knows best.
"I told my family at night: 'I will fast tomorrow as qaḍā' (a make-up fast),' but I forgot to make the intention before sleeping. Is my fast valid?"
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
The intention is obligatory in acts of worship. For obligatory fasting, the required intention is to resolve to fast during the night [before dawn]. Its proper locus is the heart, while verbalizing the intention out loud in acts of worship is a sunnah — so that the tongue may align with the heart. If the intent behind the statement in question was the intention to fast, then it is valid; but if the intent was merely to inform someone, or reflected hesitation or doubt, then it is not valid.
It is stated in *Bushrā al-Karīm* (Vol.1/P.216): "It is a sunnah to verbalize the intention — that is, whatever has already been intended in the heart, whether an obligatory or a voluntary act — such as specifying the number of rak‘ahs, just before the opening takbīr — so that the tongue may assist the heart, and because this is further removed from whispered doubts (waswasah), and in order to accommodate the view of those who held it obligatory in every act of worship that requires an intention (even though this is a minority position), by analogy with Ḥajj."
Accordingly: if the intention to fast arose in your heart before the second adhān [i.e., before Fajr], then your fast is valid.
And Allah, the Exalted, knows best.
Is it a condition that one should offer two sacrifices for a male newborn?
It is desirable to offer two sheep for a male newborn, and one for a female newborn. Offering one sheep for the male newborn is also permissible as it observes the Prophet`s Sunnah in this regard.
Is it permissible for a woman to observe voluntary fast without her husband's permission?
A woman is not permitted to observe a voluntary fast (nafl) while her husband is present without his permission.