Is it permissible to move a grave from its current location to another place, for example, from a garden in a home to a cemetery, knowing that the grave has been there for a long time, about fifty years?
It is not permissible to move the deceased from his grave, as this may result in breaking his bones and violating his sanctity. Such actions are not allowed. And Allah Knows Best.
Talking to one's fiancée in Ramadan with romantic talk may lead to arousal, and if pre-ejaculate fluid (Madhy) is discharged as a result, it does not break the fast. However, it is advised to avoid actions that provoke desire and lead to this outcome. If semen (Mani) is discharged as a result, it does break the fast.
The discharge of Madhy doesn't invalidate one's fasting but it invalidates the ablution and his clothes must be washed because they are impure in this case. As for Mani, it breaks one's fast and making up invalidataed is obligatory, beside; a Muslim suitor should abstain from these matters during Ramadan and not to degrade the holy month to this extent. And Allah Knows Best.
Is it permissible for a woman in her waiting period (Iddah) after her husband's death to leave her house and mix with non-Mahrams?
It is not permissible for a woman in her waiting period (Iddah) after the death of her husband to leave her house except for a necessity, such as for medical treatment, nor is she allowed to mix with non-Mahrams. A woman is not permitted to mix with anyone other than her husband or Mahrams, whether she is in her waiting period or not. However, there is no harm in accepting condolences from those who visit and responding to their inquiries about her well-being. And Allah Knows Best.
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.