An ability that triggers when a player casts a spell resolves before the spell that caused it to trigger. It resolves even if that spell is countered.

Vengevine's triggered ability works only if Vengevine is already in your graveyard as you finish casting your second creature spell in a turn and if it remains there until the triggered ability resolves.

Vengevine's triggered ability checks the spells you cast over the course of the entire turn, not just the ones you cast while Vengevine is in your graveyard. For example, if you cast a creature spell, then Vengevine is put into your graveyard, then you cast another creature spell, Vengevine's ability triggers.

Vengevine's ability triggers only for the second creature spell you cast in a turn. It won't trigger for the third, fourth, or so on. It also doesn't matter how many noncreature spells you cast in a turn; the ability counts only the creature spells.