What is the ruling on using moisturizing creams on the skin during the day in Ramadan?
Using moisturizing creams on the skin does not break the fast because they do not enter the body cavity (jauf). Any absorption that occurs through the skin pores does not count as entering through an open passage.
What is the ruling on swearing a false oath by the Holy Quran?
Swearing a false oath by the Holy Quran dips the oath-taker in Hellfire, and one who had done so should turn to Allah in repentance, seek His forgiveness, give back rights to whom they belong, and pay the oath expiation.
Is it permissible for the young woman to turn the suitor down if she had no feelings for him?
Yes, it is permissible for her to do so.
Is it a condition for the mosque where I‘tikaf is performed to hold Jumu‘ah prayers?
No, it is not a condition for the mosque where I‘tikaf is performed to have Jumu‘ah prayers. However, if a person vows to perform continuous I‘tikaf, and Jumu‘ah occurs within that period, then they must observe I‘tikaf in a mosque where Jumu‘ah is held so that they do not break their continuity by leaving for Friday prayer.