Does the intention (niyyah) of the principal (muwakkil) suffice for the sacrifice (dhabḥ) of the udhiyyah?
Praise be to Allah, and peace and blessings upon our master, the Messenger of Allah.
If a person appoints an agent (wakīl) to perform the slaughter (dhabḥ) on their behalf, the intention (niyyah) of the principal (the one appointing the agent) suffices, and there is no need for the agent to have this intention himself. In fact, even if the agent is unaware that he is performing the sacrifice on someone's behalf as an udhiyyah (sacrificial offering), this does not affect its validity. And Allah, the Most High, knows best.
What is the ruling on using a patch to suppress hunger or a nicotine patch while fasting?
Fasting is a great act of worship and one of the pillars of Islam. If people knew the immense reward of Ramadan, they would wish for the whole year to be Ramadan.
Whoever eats Suhoor and breaks their fast according to the Sunnah will not experience extreme hardship, making such patches unnecessary.
However, using these patches does not break the fast because they are not a source of nourishment and do not enter the body cavity (jauf) through an open passage.
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 eating or drinking during the second Adhan?
It is not permissible to eat or drink during the second Adhan because it announces the break of dawn and the obligation to start fasting. Allah Almighty says {what means}:"and eat and drink until you can discern the white streak of dawn against the blackness of night." [Al-Baqarah/187].
Whoever eats or drinks during this time invalidates their fast, and they must refrain from eating for the rest of the day and make up for the missed fast later.