Is it permissible for one who sacrifices on behalf of another, with the latter's permission, to eat from the sacrifice?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is permissible for one who sacrifices on behalf of another with his permission to eat from the sacrifice with his permission, and he takes his place in distributing its meat.
It is stated in Hashiyat al-Jamal 'ala Sharh al-Minhaj (Vol.5/P.262): 'If a person sacrifices on behalf of a living individual with his permission, does he take the place of that individual in distributing the meat, because permission for the sacrifice implies permission for distribution, or does it depend on explicit permission? There is room for consideration, but the former view is not far-fetched.' And Allah Almighty knows best."
Is it permissible to divide one mudd of fidyah between two people?
No, it is not permissible to divide one mudd between two people, because it would not count as a full meal for either of them.
What is the ruling on using a miswak (tooth-stick) during the day in Ramadan?
It is permissible to use a miswak before noon while fasting. However, according to the Shafi'i school, it is disliked (makruh) after noon in order to preserve the natural effect of fasting in the mouth, as the Prophetﷺ said in authentic hadith:
"The breath of a fasting person is more pleasant to Allah than the fragrance of musk."
What should a person, who doubts the validity of his Wudu, or over performs it, do?
One who doubts the validity of his/her Wudu while performing it should redo it until he/she is certain of having attained purity. But, if doubt was after having performed Wudu, then he/she should not pay attention to that as doubt after the end of an act of worship does not count. This is of course in case doubt was within the reasonable limits since once it goes beyond that, it becomes a whispering of the Shaytaan (devil) which he/she should ignore as the Wudu is valid.