Is it forbidden or permissible to use prayer beads gifted by a girl with whom there is no love relationship, and is reciting the Quran from a Mushaf gifted by a girl forbidden based on the invalidity of a relationship with her?

There is no harm in benefiting from a gift unless it is for a prohibited purpose, or acquired in exchange for a prohibited benefit, especially if there is no prohibited relationship between you and this girl. Nevertheless, one should be mindful of the danger of leniency in dealing with women, as stated in the prophetic tradition: "I have not left behind me a trial more harmful to men than women." And: "Beware of the world, and beware of women, for the first trial of the Children of Israel was concerning women." It is preferable to count glorifications (tasbih) with the fingers because that is what is established from the Prophet, peace and blessings be upon him.