Does the Obligatory Ritual Bath (Ghusl) Suffice in Place of Ablution (Wuḍūʾ)?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
The more prudent course is to perform ablution (wuḍūʾ) after the ritual bath (ghusl), so as to exit the difference of scholarly opinion and because the sufficiency of the ritual bath in place of ablution is contingent upon a number of conditions and requirements being met. And Allah the Almighty knows best.
Is it valid to perform Tarawih prayer at home?
It is Sunnah for a Muslim to perform Tarawih prayer in congregation at the mosque.
However, if a person sometimes prays it at home in congregation with their family for a valid reason, there is no harm in doing so.
What is the ruling on the intention of fasting, where is its place, and when is its time?
The intention is a pillar of acts of worship; it is essential, and worship is not valid without it.
Its place is in the heart, and verbalizing it is recommended so that the tongue reminds the heart. Its meaning is to be determined to abstain from nullifiers of fasting during the upcoming day with the intention of worship and obedience to Allah Almighty. This meaning is naturally present in every Muslim on every night of Ramadan, so there is no need for obsessive doubts. If one says, "I intend to fast tomorrow for the sake of Allah," it removes any doubts.
Its time is from after sunset until before the true dawn.
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.