Elder Sign - locked dice queries
Locked dice on monsters are only unlocked when the monster is collected, which happens at the end of the Investigation Phase. Note that even if you failed to solve the Adventure or Other World card, you will still collect the monster trophy as long as you completed that task. You can then use the unlocked die on your next attempt.
Adventure cards can be done in any order, even if there are multiple locks active at the same time. The physical location of the locked die doesn't really matter. If you complete a card with a locked die on it the die moves to another lock if there is one, or if there wasn't a die on the card it stays locked on the card where it is. Whether it moves or not is irrelevant; you will need to remove both locks before you can use that die again.