What is the ruling on having brotherly ties between a strange man and a strange woman, and is the former considered a Mahram (unmarriageable) to the latter?
Such a relation between a strange man and a strange woman is forbidden in Islam because it involves forbidding what Allah has allowed by marriage, and allowing what Allah has forbidden such as looking and the like. Such a relation doesn`t render any act lawful between them, thus they are forbidden to look at each other, have a Khulwah (seclusion), and travel together.
Does wiping over one's socks during ablution permissible?
If the socks were thick, then wiping over them during ablution is permissible so long as wiping conditions are observed. And Allah Knows Best.
How are those killed in wars punished with the torment of the grave if they are not buried?
The torment of the grave refers to the suffering that the deceased experiences between the day of their death and the Day of Resurrection, which is called the Barzakh period. Similarly, it includes the blessings of the grave, whether the deceased is buried or not. And Allah The Almighty Knows Best
Does bleeding from the body, such as from wounds, invalidate ablution?
Bleeding doesn't invalidate person's ablution. And Allah Knows Best.