Is the questioner considered engaged or married based on the the details she mentioned about the engagement? And is it permissible for her, Islamically, to uncover her hair in front of the suitor and to be in seclusion with him?

The marriage contract has specific formulas, and the uncle's statement: "We have accepted the marriage" could mean an actual marriage or a future engagement. If custom indicates it is an engagement, then you are a stranger to the suitor. However, if your uncle intended to finalize the contract, and he was authorized by your father or your father agreed, then the contract is valid, and its documentation is not a condition. The uncle's intention or prevailing custom can be ascertained. If the uncle intended to conclude the marriage contract, then the marriage is valid. But if custom implies only engagement by it, then it is not considered a marriage contract.