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.
Which hour coincides with the last third of the night?
This hour could be figured out by calculating the number of night hours which start at sunset, and end at dawn break, then the total is divided on three to get the result.
Should missed Sunnah prayer be made up?
Making up missed voluntary acts of worship is from Sunnah.
What should one do if they see someone deliberately eating or drinking openly during Ramadan?
They must enjoin what is right and forbid what is wrong. If they fear harm from that person, they should disapprove of it in their heart but avoid sitting with them if possible. It is also preferable to seek the help of the authorities to prevent them from doing so.