Is it permissible for one to shake hands with his uncle`s daughter?
No, it isn`t because he is a non-Mahram (Marriageable) to her.
Is it permissible for one who sacrifices on behalf of another, with the latter's permission, to eat from the sacrifice?
It is permissible for someone who sacrificed on behalf of another with their permission to eat from it with their permission, and they stand in their place (act as their representative) in distributing it.
It is stated in Nihayat al-Muhtaj ila Sharh al-Minhaj (Vol.8/P.141): "And he—meaning the one sacrificing on his own behalf, provided he has not apostatized—has the right to eat from a voluntary sacrifice and his sacrificial gift; rather, it is recommended. As for an obligatory sacrifice, it is forbidden for him to eat from it, whether it was designated as such initially or as a liability in his dhimmah. And excluded by what has preceded is if he sacrifices on behalf of another, or if he apostatized, then it is not permissible for him to eat from it, just as it is absolutely impermissible to feed a disbeliever from it."(The text I found indicates the impermissibility of eating) ???
And it is stated in Hashiyat al-Jamal ‘ala Sharh al-Manhaj (Vol.5/P.262): "If a person offers a sacrifice on behalf of a living person with their permission, does he act as their representative in distributing it—on the grounds that permission to sacrifice is permission to distribute it—or does it depend on their explicit permission? This requires consideration, but the first view is not far-fetched." And Allah the Almighty knows best.
What is the ruling of Islamic Law if the follower (maʾmūm) stands up for the third rakʿah out of forgetfulness while the imam has sat for the middle tashahhud?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
If the imam sits for the tashahhud while the follower (maʾmūm), out of forgetfulness, stands up for the third rakʿah, he is obliged to return to his sitting position, since following the imam is obligatory. In this case, no prostration of forgetfulness (sujūd al-sahw) is required of him. If, however, he fails to return, his prayer is rendered invalid.
Shaykh al-Islām Imām Zakariyyā al-Anṣārī, may Allah have mercy upon him, states: "If the follower stands up alone out of forgetfulness, he is obliged to return, since following the imam is obligatory... If he does not return, his prayer is rendered invalid, due to his departure from what is obligatory." [Asnā al-Maṭālib,Vol.1/P.190] And Allah the Almighty knows best.
Is a woman`s prayer considered invalid if non-Mahrams (marriageable men) saw her offering it?
A woman`s prayer isn`t invalidated if non-Mahrams saw her offering it, but she had better pray in isolation.
