Does saying "I adjure you to do such and such" mean "By God, do such and such"? If the person does not respond, who bears the sin? And does the one who does not respond to a request like "By God, upon everyone who hears my call, pray for us" bear a sin? And does the ruling differ between swearing an oath for something that is possible to implement and something that is not possible?

The phrase "أستحلفك" (astahlifuka) means "I ask you to swear," with the letters sin and ta denoting a request. It does not carry the force of an oath itself. Therefore, there is no sin upon one who does not respond to a request to swear an oath. As for the statement, "By Allah, upon everyone who hears my call to supplicate for us," scholars have differed on the obligation to respond to it. The majority view is that it is recommended. According to the view that fulfilling an oath is obligatory, sin falls upon the one who swore the oath and then broke it, and expiation is due from the one who swore the oath. Sin only applies to that which is within one's capability, as Allah the Almighty says: "Allah does not burden a soul beyond its capacity" (Quran 2:286), and "He has not placed upon you in religion any difficulty" (Quran 22:78).