Does burping (belching) break the fast?
Burping does not break the fast. However, if anything comes up from the stomach, the fasting person must spit it out and rinse their mouth to cleanse it.
If they swallow it intentionally while being able to expel it, or if they swallow their saliva before rinsing their mouth, their fast is invalidated.
What is the virtue of Laylat al-Qadr?
It is enough to know its great status that Allah revealed an entire surah about it—Surah Al-Qadr. Moreover, the Quran was first revealed on this night.
Allah says {what means}:
"We have indeed revealed this (Message) in the Night of Power: And what will explain to thee what the night of power is? The Night of Power is better than a thousand months. Therein come down the angels and the Spirit by Allah's permission, on every errand: Peace!... This until the rise of morn!" [Al-Qadr/1-5]
The Prophet ﷺ taught us to observe I‘tikaf in the last ten nights of Ramadan, seeking Laylat al-Qadr. Whoever worships Allah and revives this night will receive the reward of worshiping for a thousand months—excluding Laylat al-Qadr itself.
Is the son of the sister by breastfeeding considered a mahram in Islam, and is it permissible for a woman to go for Hajj with him?
Everything that is prohibited by lineage is also prohibited by breastfeeding. The son of the sister by breastfeeding is considered a mahram, just like the son of the sister by blood, and it is permissible for him to be her mahram for Hajj and Umrah. And Allah Knows Best.
Is there a solution to put an end to thinking of worries during prayer?
Firstly, make ablution after the time for prayer begins and busy yourself with remembering Allah, The Exalted, before the iqaamah (start of prayer).In order to become humbly submissive during prayer, you must perform prayer in congregation. After the prayer ends, stay in your place and read the post-prayer remembrances (Adhkaar) and make supplication to Allah, The Exalted.