Does vomiting during the day in Ramadan break the fast?
Intentional vomiting is one of the nullifiers of fasting; whoever vomits deliberately breaks their fast.
However, if vomiting occurs involuntarily, the fast remains valid as long as nothing returns to the body cavity (jauf). If anything is swallowed back, the fast is invalidated.
The Prophet ﷺ said: "Whoever is overcome by vomiting does not have to make up the fast, but whoever induces vomiting deliberately must make it up." [Narrated by Abu Dawood and At-Tirmidhi]
When is supplication (du‘a) more likely to be accepted: before or after breaking the fast in Ramadan?
Du‘a is accepted at all times, and this is part of Allah’s mercy and generosity toward His servants.
The Prophet ﷺ said: "No Muslim makes a supplication that does not involve sin or severing family ties except that Allah grants them one of three things: either He grants their supplication immediately, or He stores it for them in the Hereafter, or He averts from them an equivalent harm." [Narrated by Ahmad]
However, in Ramadan, du‘a is especially likely to be accepted shortly before breaking the fast.
The Prophet ﷺ said: "Three supplications are never rejected: the supplication of a fasting person until they break their fast, the supplication of a just leader, and the supplication of an oppressed person. Allah raises it above the clouds, opens the gates of heaven for it, and says: ‘By My might, I will surely grant you victory, even if after a while.’" [Narrated by Al-Tirmidhi]
What is the ruling on discharges two or three days before the expected period of menstruation and the light-colored blood accompanying it? Must the woman abstain from prayer during this period?
If the total duration of these blood-tinged discharges reaches a day and a night (24 hours) or more, it is considered menstruation. If their total does not exceed 24 hours, it is not considered menstruation but is irregular bleeding (dam al-fasad). Each woman has specific cases for which she should ask the scholars. And Allah the Almighty knows best.
Is it permissible to offer mandatory prayer while sitting?
All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions. Standing up is a pillar in the mandatory prayer and the prayer is not valid without it unless one cannot do it. As for Nafila (supererogatory prayer), one can perform it in the state of sitting even if he/she can stand, but his/her reward is half the reward of the person who prays while standing if he/sh has no legal excuse for such an act. And Allah Knows Best.