Is it permissible for a girl to marry her paternal uncle (her father’s brother from his mother’s side), and is it permissible for her to uncover her hair in front of him?

Your father's brother from the mother's side is considered your paternal uncle (عم) according to Islamic law and is one of your mahrams. Brotherhood includes full-siblings, half-siblings from the father's side, or half-siblings from the mother's side. The proof for this is Allah Almighty's saying: "And your sisters."

If he were a foster uncle (meaning he shared fosterage with your father from one woman), then he is also mahram (definition) to you, based on the Prophet Muhammad (peace be upon him) saying: "What is forbidden by lineage is forbidden by fosterage."

Contrary to what was mentioned [elsewhere], the brother from the mother's side inherits from his brother or sister if his right is not forfeited. His share is one-sixth if he is alone, and one-third if there are multiple, with the male and female shares being equal.

Scholars are in consensus that siblings from the mother's side inherit one-sixth for an individual and one-third for multiple individuals, and they do not inherit in the presence of the father, grandfather, sons, or grandsons. This is based on Allah Almighty's saying: "And if a man or a woman leaves no direct heir but has a brother or a sister [from the mother's side]."

Therefore, your uncle from the mother's side is a mahram to you; it is not permissible to marry him, and he is permitted to see what a man may see of his female mahrams.