What is the ruling on a Muslim who slaughters an animal while being in a state of Janabah (ritual impurity)?
All Perfect Praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upo all of his family and companions.
Slaughtering is permissible for the ritually impure man and the menstruating woman because ritual purity isn`t a condition for the validity of the slaughtering. Moreover, it is permissible for the uncircumcised person to do the slaughtering as well. And Allah The Almighy Knows Best.
What should a person who doubted having missed a pillar of prayer do?
All praise be to Allah, The Lord of The Worlds. The prayer of one who doubts having missed one of its pillars is valid, and nothing is due on him/her since having a doubt after offering the act of worship doesn`t undermine its validity. And Allah Knows Best.
After I had prayed, I found a drop of menstrual blood and was unsure when that happened; what is the ruling on my prayer and fast?
All praise is due to Allah, peace and blessing be upon the Messenger of Allah.
Your prayer and fast are correct ,and you should not make up for them, and we ask Allah, The Almighty, to duely reward you for these acts of worship. Your menses start once you see blood because the situation remains as such unless there is certainty or predominant conjecture, as per the Fiqh maxim: "Certainty is not removed by doubt". And Allah Knows Best.
A person owns sheep or goats and occasionally feeds them from the grass in other people's orchards without the owners’ permission. Is it permissible to eat the meat of these animals if invited to do so? Is it permissible to purchase from these sheep whose owner feed them from people's orchards without their permission, and can one accept gifts from them, such as meat or milk?
Yes, it is permissible because the one who is accountable is their owner, and the cost of the grass on his accountability. In addition, in order to be on the safe side you should abstain from eating his products, because his sheep case is as if they were fed on impurities. And Allah Knows Best.