Is it obligatory to have the intention for each day of fasting, or is one intention sufficient for the whole month?
The intention is obligatory for each day of Ramadan because each day is an independent act of worship separate from the others.
The intention must be made at night before the break of dawn, as the Prophetﷺ said: "Whoever does not intend fasting at night, there is no fast for him." [An-Nasa’i]
And he also said: "Whoever does not firmly resolve to fast before dawn, there is no fast for him." [At-Tirmidhi, Abu Dawood, and An-Nasa’i]
Whoever wakes up and eats Suhoor while mindful of fasting has made the intention. Likewise, one who firmly intends at any moment during the night to fast the next day has also fulfilled the intention.
I bought an apartment, and I am saving money to pay the remaining balance of its price — is zakāh obligatory on this money?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Zakāh is obligatory on all saved/hoarded wealth. Once the total wealth reaches the niṣāb (minimum threshold liable for zakah— equivalent to the value of 85 grams of pure 24-karat gold) and a full ḥawl (lunar year) has elapsed over it, zakāh becomes obligatory at a rate of (2.5%) — even if the wealth is earmarked for basic future needs, and even if the wealth's owner is in debt. Debt does not prevent the obligation of zakāh, nor is it deducted when calculating the zakāh due, based on the general and unrestricted wording of all the Qur'anic verses commanding zakāh, which draw no distinction between someone in debt and anyone else.
It is stated in ‘Umdat as-Sālik, from the books of the Shāfi‘ī school: "If someone possesses exactly the niṣāb, and owes an equivalent amount in debt, zakāh remains obligatory on what is in his possession, and the debt does not prevent this obligation" — meaning, the obligation of zakāh on what is presently in his possession.
The ḥawl (annual cycle) recognized for zakāh, as well as for the other sharī‘ah obligations that Allah, the Exalted, has imposed upon Muslims, is the Hijrī (lunar) year. And Allah, the Exalted, knows best.
What is the ruling on shaving the head of the newborn?
It is desirable to shave the head of the newborn on the seventh day from delivery, and the weight of his/her hair is given in gold , or silver as charity.
Is it permissible for a woman to wear underwear while performing Umrah?
Yes, it is permissible for a woman to wear underwear while performing Umrah. This is because she should keep her regular clothes that cover all her body while being in a state of Ihram (ritual consecration) for Hajj, or Umrah. However, she should uncover her face and hands, but it is permissible for her to let her head-covering garment drape from her head down over her face when non-Mahram (i.e., marriageable) men pass by her. And Allah Knows Best.