What is the ruling of Islamic Law on saying the basmalah at the beginning of wudu`?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Saying the basmalah (Bismillāh) at the beginning of wuḍūʾ is a sunnah. It is stated in al-Minhāj al-Qawīm Sharḥ al-Muqaddimah al-Ḥaḍramiyyah (p. 27): “Its sunnahs include the siwāk, then the tasmiyah (saying Bismillāh), joined with the intention (niyyah), at the start of washing the hands.” And Allah Almighty knows best.
What is the ruling on vomiting, and does it invalidate ablution?
Vomit is impure (najis). Its exit is not considered one of the nullifiers of ablution. However, the mouth must be washed and purified from it, and any that gets on clothing or the body must be washed for prayer, because prayer is not valid with impurity present on the body or clothing. And Allah the Almighty knows best.
Does using a wet miswak while fasting break the fast?
A fasting person should ensure that the miswak is dry when using it.
However, if the miswak is slightly moist but does not release any liquid when squeezed, then its use does not break the fast.
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.