Is it permissible for the young woman to turn the suitor down if she had no feelings for him?
Yes, it is permissible for her to do so.
What is the monetary value for the expiation of an oath (Kaffarat al-Yamin)?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
The expiation for an oath (Kaffarat al-Yamin) consists of feeding ten (10) needy persons. This is estimated at 600 grams of rice per person. It is also permissible to pay its value in cash, which is estimated at one dinar (per person). And Allah the Exalted knows best.
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.
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.