Is what occurred between the questioner and the man — an offer and acceptance in which she gave herself to him and he gave himself to her — considered a legally valid marriage that would prevent her from marrying her deceased husband in the afterlife?

The relationship between a man and an unrelated woman outside the framework of marriage is forbidden. What occurred between you is not a valid marriage, as a sound marriage requires the permission of the guardian and two witnesses, based on the Prophet's (peace be upon him) saying: "There is no marriage except with a guardian and two just witnesses," and his saying: "Any woman who marries without the permission of her guardian, her marriage is invalid." To meet your husband in Paradise, he must be among the people of Paradise, and you must be righteous, as Allah Almighty says: {Gardens of perpetual residence; they will enter them with whoever were righteous among their fathers, their spouses and their descendants.} It is also required that you do not marry after him, based on Hudhayfah's statement to his wife: "If you wish to be my wife in Paradise, then do not marry after me, for a woman in Paradise belongs to her last husband in this world."