Does the utterance of the word "every" and the phrase "anything" constitute a vow that necessitates donating any physical item given by the sister, given the intention of making a vow? And can one be absolved of this vow by believing that what the sister gives away still belongs to her, and thus the vow is not binding on me since I do not own it?

The malady of waswasa (whispers/obsessive thoughts) is treated by completely ignoring it. Ibn Hajar al-Haytami was asked about the cure for waswasa, and he replied: "It has an effective remedy, which is to completely and sufficiently disregard it, even if there is much hesitation in one's soul. For whenever one does not pay attention to it, it will not persist; rather, it will vanish after a short time, as those who were successful have experienced." As for whoever lends an ear to it, it will increase in them until it drives them to the brink of insanity. Waswasa comes from Satan; "Indeed, Satan is an enemy to you, so take him as an enemy." Al-Izz ibn Abd al-Salam and others mentioned that the cure for waswasa is to believe that it is a satanic thought, and that Iblis is the one who instilled it, and fighting it will earn one the reward of a mujahid (striver in God's path).