What is the ruling on using toothpaste during the day in Ramadan?
Using toothpaste does not break the fast as long as nothing reaches the body cavity. However, it is disliked (makruh).
It is preferable for a fasting person to use it before the time of fast starts or after Iftar (breaking the fast) to avoid risking their fast.
What is the ruling on performing Tahajjud after the Witr?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is permissible for one who has prayed the Witr to perform voluntary (Nafl) prayers after it. However, it is preferable for the Witr to be the final prayer of the night. Therefore, if a person is confident that they will wake up during the night for Tahajjud, it is recommended for them to delay the Witr until after the Tahajjud. Conversely, if one fears they may not wake up, they should perform the Witr before sleeping.
Al-Khatib al-Shirbini (may Allah have mercy on him) stated: 'It is not disliked (Makruh) to perform Tahajjud after the Witr, but it is not recommended to do so intentionally.' [Mughni al-Muhtaj, Vol. 1/P.454]. And Allah the Exalted knows best."
Can I start fasting based on the moon sighting of another country?
You must follow the moon sighting of the country you are in.
What is the ruling on someone who possesses cash reaching the niṣāb (minimum threshold liable for zakah), and then uses part of it to purchase gold before the ḥawl (lunar year) is complete — must he pay zakāh on all of it [combined], or only on the remaining cash, excluding the gold?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Gold acquired for hoarding and saving is subject to zakāh once it reaches the niṣāb (minimum threshold liable for Zakah) — when combined with any cash held — and once a full ḥawl (lunar year) has elapsed over it. The starting point for calculating this ḥawl is the ḥawl of the paper currency [used to purchase it], which had already reached the niṣāb and was then used to purchase the gold.
It is stated in Mughnī al-Muḥtāj (Vol.2/p.78): "As for someone who sells silver in exchange for gold, or vice versa, zakāh remains obligatory upon it, since he builds [the calculation of] its ḥawl upon [the ḥawl established at the time of] the original transaction [i.e., when the wealth was first acquired]."
This has already been explained in detail in Fatwa No.
2670 — please refer to it.
And Allah, the Exalted, knows best.