Was what transpired an engagement or a legitimate marriage contract, what are the boundaries of the relationship between an engaged couple, and is intention obligatory for the completion of the engagement?

What transpired between the questioner's uncle and the young man's grandfather was not a valid marital contract (aqd shar'i for marriage), but merely an engagement (khitbah). This is because marriage has its specific legal formula, which includes offer (ijab) and acceptance (qabul). Consequently, the questioner remains a non-mahram (ajnabiyah) to this young man until a valid marital contract is concluded between them.