Is it permissible for the guardian to give Sadaqa (voluntary charity) from the money of the orphans?
It is impermissible for the guardian to donate from the money of the orphans because he is entrusted with the safekeeping of that money, and is prohibited from donating it.
Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
Is it permissible to authorize charitable organizations to perform the Udhiyah on one`s behalf?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is permissible to authorize charitable organizations to perform the sacrifice (Udhiyah) on one’s behalf. However, if these organizations undertake the slaughtering for a group of people, those in charge of the slaughtering must maintain lists of the names of those who authorized them. Furthermore, at the time of slaughter, the slaughterer must intend that the specific sacrifice is on behalf of a specific person. And Allah the Almighty knows best.
Is the niṣāb calculated based on the price of 21-karat gold, or 24-karat gold?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Zakāh is obligatory on cash and on gold designated for saving or for trade, provided the total reaches the niṣāb (minimum threshold liable for zakah), and a full ḥawl (lunar year) has elapsed over it. The niṣāb is (85) grams of 24-karat gold; for 21-karat gold, the niṣāb equals (97) grams; and for 18-karat gold, it equals (113) grams.
The relied-upon position is to calculate the zakāh based on the buying price [i.e., the price the gold merchant would pay the owner to purchase the gold from him] on the day the zakāh obligation is due.
The one paying zakāh may assess/calculate the niṣāb using any of the aforementioned gold karats [i.e., he may choose whichever karat standard he wishes for the purpose of the calculation]. And Allah, the Exalted, knows best.