What is the ruling on one who sees moisture on his clothes and doubts whether it is semen or pre-seminal fluid (madhy)?
Whoever finds moisture upon waking from sleep and doubts whether it is semen or madhy, and cannot distinguish between them, he may choose between them and act according to his choice. If he wishes, he can consider it semen and perform the ritual bath, or consider it madhy, perform ablution, and wash what it has soiled. This is because if he fulfills the requirement of one of them, he is definitively free from it, and the default is his innocence from the other. And Allah the Almighty knows best.
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.
Does Laylat al-Qadr move between the nights of Ramadan?
Laylat al-Qadr is definitely in Ramadan, and it is most likely in the last ten nights, especially on the odd-numbered nights.
For this reason, the Prophet ﷺ commanded observing worship in the last ten nights, and he himself used to dedicate those nights to worship. Many people put special effort into the 27th night of Ramadan, and they are rewarded in any case, whether they actually coincide with Laylat al-Qadr or not, because worshiping on any night of Ramadan carries great rewards.
I vowed to give a specific charity if a certain matter came to pass — what is the ruling on giving that charity before the matter is realised?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
Fulfilling a vow (nadhr) is obligatory, in accordance with the word of Allah the Almighty: "And let them fulfil their vows." [Al-Ḥajj/ 29] And the saying of our master the Messenger of Allah ﷺ: "Whoever vows to obey Allah, let him obey Him; and whoever vows to disobey Him, let him not disobey Him." (Reported by al-Bukhārī.)
The Shāfiʿī scholars distinguished between a financial vow (nadhr mālī) and a bodily vow (nadhr badanī). They permitted the fulfilment of a financial vow to be brought forward — before the stipulated condition is met — but did not permit the same for a bodily vow, which may only be fulfilled after the condition has actually been realised.
Shaykh al-Islām Imām Zakariyyā al-Anṣārī, may Allah have mercy upon him, states: "It is permissible to bring forward the fulfilment of a financial vow before the condition stipulated in it is met — such as saying: 'If I am healed, I vow to free a slave' or 'to give such-and-such in charity' — just as it is permissible to pay zakāh in advance. This is unlike a bodily vow, such as fasting." [Asnā al-Maṭālib, vol. 4/P.246]
Imām al-Bājūrī, may Allah have mercy upon him, states: "Like expiation other than fasting, a financial vow — such as saying: 'If Allah heals my sick one, I vow to free a slave for the sake of Allah,' or 'If Allah heals my sick one, I vow to free a slave on the Friday following the recovery' — it is permissible to bring it forward before the recovery in the first case, and before the Friday following the recovery in the second case." [Ḥāshiyat al-Bājūrī ʿalā Sharḥ Ibn Qāsim, Vol.2/P.596] And Allah the Almighty knows best.