Is it permissible to kiss the hands of leaders of the Islamic world or to bow to them out of respect, and what is the correct way to greet them, given that the common practice among men is embracing and shaking hands?

The greeting for people of knowledge is by extending greetings and shaking hands. It is also permissible sometimes to kiss the head and hand, without making it a habit. As for embracing, it is permissible upon returning from a journey, after a long absence, or due to intense love for the sake of Allah, and the proof for this is the action of the Prophet (peace be upon him). Bowing and prostrating to other than Allah is not permissible, because it is an act of worship that is due to Allah alone.