Is the one offering the sacrifice liable if its meat spoils?
Praise be to Allah, and prayers and peace be upon our Master the Messenger of Allah.
If the meat (of the sacrifice) spoils due to the negligence of the one offering the sacrifice in preserving it, or due to improper storage, then he is liable to compensate for the portion due to the poor (which is estimated as half a kilogram of meat). If the sacrifice was a vowed (mandatory) one, then he is liable for all of it.
However, if he was not negligent, then there is no liability upon him, because its ruling is the ruling of a trust (like an item left in someone's care). And Allah Almighty knows best.
What is the ruling on using toothpaste during the day in Ramadan?
Using toothpaste does not break the fast as long as nothing reaches the body cavity. However, it is disliked (makruh).
It is preferable for a fasting person to use it before the time of fast starts or after Iftar (breaking the fast) to avoid risking their fast.
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.
Is it permissible to make ablution without answering the call of nature after waking up?
Washing front and back openings (Istinjaa`) is not a condition for the validity of ablution because it is done to remove Najaasah (impurity), thus if there is no Najaasah, there is no need for that, and then it is permissible to make ablution without answering the call of nature. However, prayer is invalidated if there is Najaasah on the anus ,or the front opening, so it (Najaasah) must be removed for the prayer to become valid, and not the ablution.