Is it permissible to distribute the raw meat of the vowed animal sacrifice amongst the poor/to offer it to them in cooked form?

It is impermissible for the vow-maker to eat from the vowed animal sacrifice, rather, he/she should distribute it as he/she had intended upon making the vow, but if the vow was a general one, without any specification then, it is better to give it as raw meat.

What is the ruling when the duration of the monthly period varies, and sporadically increases?

If the period didn`t exceed (15) days from the first seeing of blood discharges until its end including the times of temporary cessation, then it is menses. But, if the period exceeded (15) days, then the woman experiencing this is Mostahadah (bleeding outside the time of monthly period), and should abide by her regular period, and consult one of the scholars.

Should the father command his ten-year-old daughter to wear the Islamic dress?

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.

The father should order his daughter to put on the Islamic dress once she turns ten, in order for her to get used to it. And Allah Knows Best.

Is it permissible for a woman to ride a taxi without a Mahram (unmarriageable kin) in order to attend a gathering of knowledge?

It is permissible for the woman to pursue the knowledge that she needs in order to perform the religious requirements due on her if there was nobody to teach her at home, provided that there is no temptation involved. Moreover, we don`t recommend that she rides a taxi without a Mahram although such an act isn`t from the forbidden Khulwah (seclusion).