Is what is mentioned true, that the graves of the two companions Hudhayfah al-Yamani and Jabir ibn Abdullah were exhumed in Iraq in 1934, and that their faces appeared perfectly intact after 1300 years, and is it permissible to exhume graves for this reason?

The story mentioned is of unknown authenticity. As for digging up a grave, the basic principle is that it is not permissible, due to the sanctity of the deceased, based on the Prophet's (peace and blessings be upon him) saying: "Breaking the bone of a dead person is like breaking it when he is alive." This is unless there is a clear benefit determined by the legitimate ruler.