It means that this Digimon can no longer leave the battle area by processing other than deletion. Such processing includes "return to the hand/deck," "place in the security stack," and "place under another Digimon or Tamer." It only leaves the battle area by deletion.

No, the card is trashed. Digimon without DP can't be in the battle area according to the rules, therefore upon the rule check timing, the card is considered a card that doesn't belong in the battle area and is trashed. This is why that card is trashed even if that Digimon is affected by this card's [Start of Your Main Phase] effect.