Which is better during the day in Ramadan: reciting the Quran or performing voluntary prayers?
A Muslim should establish a daily schedule for reciting the Quran in Ramadan.
Once they have completed their daily portion (known as a wird or hizb), they can engage in other acts of worship, including voluntary prayers (nawafil). Prayer itself is called "Quran", because a significant part of it involves reciting the Quran.
Allah says: "BE CONSTANT in [thy] prayer from the time when the sun has passed its zenith till the darkness of night, and [be ever mindful of its] recitation at dawn: for, behold, the recitation [of prayer] at dawn is indeed witnessed [by all that is holy]." [Al-Isra`/78]
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."
Does excessive sleep during Ramadan invalidate fasting?
Sleeping a lot in Ramadan does not invalidate the fast, but a Muslim may miss out on great rewards from prayer, Quran recitation, and acts of worship due to excessive sleep.
What is the ruling on praying in congregation at the mosque?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Congregational prayer (Salat al-Jama‘ah) is a communal obligation (Fard Kifayah) for resident men regarding the performance of the prescribed (obligatory) prayers. For men, praying in congregation at the mosque is better than praying elsewhere, such as at home. On the authority of Abdullah bin Umar, the Messenger of Allah ﷺ said: 'Prayer in congregation is twenty-seven degrees more excellent than the prayer of a person alone' (Reported by Bukhari & Muslim). Furthermore, on the authority of Abu Hurayrah, the Messenger of Allah ﷺ said: 'Shall I not tell you that by which Allah erases sins and raises ranks?' They said, 'Of course, O Messenger of Allah.' He said: 'Performing wudu thoroughly despite difficulties, taking many steps toward the mosques, and waiting for the next prayer after the prayer; that is your Ribat (steadfastness)' (Narrated by Muslim).
As for a woman, her praying in congregation at home is better for her than in the mosque, according to the saying of our Master the Prophet ﷺ: 'Do not prevent your women from attending the mosques, but their homes are better for them' (Narrated by Abu Dawood). Young boys should be encouraged to attend the mosques and congregational prayers so they may become accustomed to them. And Allah the Exalted knows best.