Is it permissible to fast on behalf of the dead who died owing missed fast to make up?
His relative should fast on his behalf, and it is permissible for the guardians to give permission to non-relatives of the dead to fast on his behalf as well. And Allah Knows Best.
What should a sick person, who is incapable of fasting, and who didn`t make up for missed fasting days, do?
One who has missed fasting days is obliged to make up for them, but if he/she wasn`t able to because of an incurable disease , or old age, then he/she has to pay a ransom which is feeding a needy person for each of the missed fasting days. And Allah Knows Best.
Sometimes I receive a message containing a picture of someone desecrating the Noble Quran. The sender asks recipients to send that message to their contacts as an act of defending the Quran. What should I do when receiving such messages?
Praise be to Allah, the Lord of the Worlds.
You don`t have to circulate that message, because this isn`t the proper way to defend the Quran. And Allah The Almighty Knows Best.
Is it permissible to offer an absentee funeral prayer?
Yes, it is permissible to offer an absentee funeral prayer.