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 ruling on ablution without istinja' after sleep?
The sleep of one whose buttocks are not firmly seated on the ground invalidates ablution. Whoever wakes up and wants to pray must perform ablution only. Istinja' is not a condition for the validity of ablution, because it is for removing impurity from the private part. If there is no impurity on the private part, then istinja' is neither obligatory nor recommended. And Allah the Almighty knows best.
What is the ruling on the use of an inhaler by a *muḥrim* (a person in the state of *iḥrām*)? [An inhaler is a medicinal device used for inhalation, containing various herbal ingredients.]؟
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is permissible for the muḥrim (a person in the state of iḥrām) to use incense (bakhūr), sprays, and inhalers that contain aromatic substances for the purpose of treatment, because the intention is medical treatment, not the use of perfume (taṭayyub). No expiation (fidyah) is required of him for doing so.
It is stated in Ḥāshiyat al-Bujayrimī ʿalā al-Khaṭīb (Vol.2/p.455): “That which is intended for eating or for medical treatment, even if it has a pleasant scent, such as apples, spikenard (sunbul), and the various fragrant spices such as mastic (muṣṭakā), is not forbidden, and no fidyah is due for it, because what is intended for eating or treatment carries no fidyah.”. And Allah Almighty knows best.
Is it permissible to pay the Zakah (obligatory charity) for settling the debt of a deceased relative?
It is impermissible to pay the Zakah for settling the debt of the deceased since Zakah is paid to eligible recipients who are alive. As for the debts of the deceased, they are to be settled from the estate before dividing it amongst the heirs, but if the deceased didn`t leave an estate, then it is desirable for his/her heirs to settle those debts if they can afford them. And Allah Knows Best.