What should one who doubts the validity of his ablution and performs it frequently do?
Whoever doubts the validity of his ablution after finishing it, his ablution is valid. This is because the default is the validity of the ablution, and because doubt after finishing an act of worship doesn`t affect its validity. And Allah the Almighty knows best.
Is it permissible to slaughter one animal as a sacrifice and an Aqeeqah (the sheep slaughtered on the seventh day from the child`s birth)?
It is impermissible to do so since each of them is slaughtered for a different reason.
What is recommended for a Muslim to say on Laylat al-Qadr?
On Laylat al-Qadr, it is recommended for a Muslim to recite the supplication (du‘a) that the Prophet ﷺ taught Aisha (may Allah be pleased with her):
"O Allah, You are Most Forgiving, and You love forgiveness, so forgive me." [Narrated by Al-Tirmidhi]
What is the ruling on someone who eats or drinks thinking that the sun has set, then realizes that it has not yet set?
Whoever eats or drinks believing that the sun has set, then later discovers that it has not yet set, their fast is invalid, and they must make up that day after Ramadan. It is not permissible to break the fast before confirming sunset—either by seeing it, through personal reasoning, or by relying on the statement of someone trustworthy in their religious commitment.