What should the one performing the slaughter say at the time of slaughtering the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is Sunnah to say the following supplication at the time of slaughtering the 'aqīqah:
"Bismillāhi wallāhu Akbar, Allāhumma laka wa ilayka, hādhihi 'aqīqatu fulān."
("In the name of Allah, and Allah is the Greatest. O Allah, this is for You and unto You — this is the 'aqīqah of [the child's name].")
This is based on what al-Bayhaqī narrated in Al-Sunan al-Kubrā (Vol.9/P.511), that the Prophet ﷺ said: "Slaughter it in his name and say: In the name of Allah, and Allah is the Greatest. O Allah, this is for You and unto You — this is the 'aqīqah of so-and-so."
And Allah Almighty knows best.
What are the Sharia consequences when the sacrificial time for the uḍḥiyyah comes to an end?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
If the sun sets at the end of the last of the Days of Tashrīq and the sacrificial animal (uḍḥiyyah) has not yet been slaughtered, then its prescribed time has elapsed. Should one slaughter it thereafter, it will not be considered a valid uḍḥiyyah.
However, if the sacrifice was vowed (mandhūrah), then it remains obligatory to slaughter it — and it shall be carried out as a make-up (qaḍā') of the vow, with its meat distributed in the rightful channels designated for such sacrifices.
It is stated in Bushrā al-Karīm (p. 702): "If one slaughters after the sunset of the last of the Days of Tashrīq... it isn`t considered a valid uḍḥiyyah, unless it was vowed — in which case it is carried out as qaḍā'."
And Allah Almighty knows best.
What is the ruling on swallowing saliva while fasting?
It is permissible for a fasting person to swallow their saliva because avoiding it would cause undue hardship and excessive strictness in religion. Islam discourages such excessiveness since Allah the Almighty intends ease for His followers and does not intend to put them in hardship.
Is my husband entitled to take my salary?
Your salary is yours, and you may give some of it to him as a kind of free-will contribution.