Is it permissible for someone to make a supplication to Allah to marry an already married, or an engaged woman?
No, it isn`t, and the person who does so is sinful before Allah, The Almighty.
Is it a condition that the meat of the Eid sacrifice should be distributed in order for the sacrifice to be accepted by Allah?
The poor and needy should be given from that sacrifice , even if it be a small portion,(One kilo for example) as raw meat so that they would cook it the way they want. The remainder of that sacrifice is either distributed, eaten, or offered to people in a banquette .
Is it obligatory for a wife who has been abandoned for many years to observe the waiting period (iddah) after her husband passes away?
If her husband passes away, the wife is required to observe the waiting period (Iddah), even if he had abandoned her, because she is his wife and inherits from him, so she must observe the iddah after his death. And Allah Knows Best.
Is it permissible for a teacher to have one of the school meals originally allocated to students considering that there is plenty of them and they may spoil?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
The Ministry of Education has the final say in this regard because it isn`t allowed to take from public funds save with the permission of the body in charge of spending from it. In fact, we have sent a letter to the Ministry concerning this issue and we are waiting for an answer. However, to prevent spoilage of the meals, they can be sold and the price kept in favor of the students or distributed amongst the students themselves. And Allah The Almighty Knows Best.