What is the extent of my relationship with my paternal uncle and its legitimate boundaries?

The paternal uncle must be honored, respected, and shown kinship. He is a mahram (a unmarriageable kin), so it is permissible to shake his hand, be alone with him, and travel with him. It is permissible for a woman to show him what is usually uncovered during her daily activities, such as her face, hands, and forearms, provided there is no fear of fitnah (temptation) and no suspicion.