Does a possible understanding of the rules of modesty mean that men should squat or bow when urinating, and is it more modest not to use a urinal in a men's room if one is Muslim and his room is close to the restroom?

Islamic Sharia (definition) cares for all aspects of life, including the etiquettes of relieving oneself, which include: not facing the Qiblah, not touching the private parts with the right hand or cleaning oneself with it, relieving oneself while sitting, concealing oneself from people's eyes, and not uncovering the 'awrah except when close to the ground. It also includes etiquettes such as: uttering supplications upon entering and exiting the lavatory, meticulously removing impurities, removing impurities three times or an odd number of times, not using bones or dung for Istijmar (cleaning oneself with stones or other dry materials), not urinating in stagnant water, not urinating in people's pathways or their shade, and not greeting someone who is relieving themselves or returning a greeting in that situation.