Does using a wet miswak while fasting break the fast?
A fasting person should ensure that the miswak is dry when using it.
However, if the miswak is slightly moist but does not release any liquid when squeezed, then its use does not break the fast.
Is it permissible to eat from an Udhiyah slaughtered on behalf of a deceased person?
Praise be to Allah, and prayers and peace be upon our Master the Messenger of Allah.
It is permissible to eat from the sacrifice (uḍḥiyyah) that is offered on behalf of a deceased person. This is the madhhab (school of thought) of the Hanbalis. In this case, the heirs take the place of the deceased as if he were alive, with the same rights to eat from it, give it in charity, and offer it as a gift.
It is stated in Maṭālib Uli al-Nuhā (Vol.2/P.472): "Offering a sacrifice on behalf of a deceased person is better than offering one on behalf of a living person, because the deceased is unable (to perform deeds) and is in need of reward. It is to be treated like a sacrifice on behalf of a living person in terms of eating, giving charity, and giving gifts." And Allah Almighty knows best.
Is it permissible to offer an absentee funeral prayer?
Yes, it is permissible to offer an absentee funeral prayer.
What should someone do whose gums are bleeding?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Whoever experiences bleeding gums while fasting must spit until his saliva runs clear — that is, until the bleeding has stopped — and then rinse his mouth to purify it.
If any of the blood enters his internal cavity (jawf) unintentionally, then his fast remains valid. And Allah, the Exalted, knows best.