Is it permissible to bow before an elder out of respect, and is it necessary to do so to win the favor of the father of a desired girl for marriage, especially if this is a common custom in the town and the father insists on it?

The fundamental way to greet is by shaking hands. Embracing is permissible after a long absence or journey. However, bowing upon meeting is not allowed, whether to a Muslim or a disbeliever, or to a king or a relative, because it involves a humiliation that is due only to Allah Almighty, and it resembles the practice of non-Arabs. The Prophet, peace and blessings be upon him, forbade bowing, and the majority of scholars prohibit it. The prohibition becomes more severe if the bowing approaches prostration, and it becomes disbelief if it is intended to glorify the created being as Allah is glorified.