Is it disliked to clip one`s nails at night, and is it permissible to burn them afterwards?

It is desirable to bury the cut hair and the clipped nails. As for burning clipped nails, there is no evidence forbidding that , but it is better to suffice with the aforesaid ruling-burying cut hair and clipped nails-as it is based on a well known evidence.

Is it permissible to pay the expiation of an oath to a charitable party as it feeds the poor and needy such as Tkiyet Um Ali?

All perfect praise be to Allah, The Lord of The Worlds, and May His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.

There is no harm on authorizing someone to handle the expiation of another to the poor and needy, since Shafiee's jurists stated that authorizing someone for the purpose of distributing Zakah, expiation and vow is permissible as stated in [Mughni Al-Muhtajj, vol.3 pp.237]. At last, the intention of the person who intends to authorize someone else suffices in this regard. And Allah Knows Best.

Is Aqeeqah due on the miscarried embryo?

No Aqeeqah is due on the dead embryo.

Is it permissible for a father to divide his property amongst his children except one under the pretext that he has paid for the latter`s tuition? This is knowing that his other children were given the opportunity to pursue their education but didn`t because they were educationally poor. Moreover, is he allowed to give his other children who have helped him with growing his business?