Q1: What does "while you have (the specified card) on the field" mean, exactly?
It refers to when you have the specified card in the battle area or breeding area.
Our Courage United ST20-14 C ADVENTURE While you have a Digimon or Tamer with the [ADVENTURE] trait on the field, you can ignore this card's color requirements. [Main] <Draw 2>. (Draw 2 cards from your deck.) Then, place this card in the battle area. [All Turns] When any of your level 5 or higher Digimon would leave the battle area, <Delay> (By trashing this card after the placing turn, activate the effect.) • You may play 1 level 5 or lower Digimon card with the [ADVENTURE] trait from your hand without paying the cost. --- [Security] Place this card in the battle area.
Our Courage United ST20-14 C ADVENTURE While you have a Digimon or Tamer with the [ADVENTURE] trait on the field, you can ignore this card's color requirements. [Main] <Draw 2>. (Draw 2 cards from your deck.) Then, place this card in the battle area. [All Turns] When any of your level 5 or higher Digimon would leave the battle area, <Delay> (By trashing this card after the placing turn, activate the effect.) • You may play 1 level 5 or lower Digimon card with the [ADVENTURE] trait from your hand without paying the cost. --- [Security] Place this card in the battle area.
Our Courage United ST20-14 C ADVENTURE While you have a Digimon or Tamer with the [ADVENTURE] trait on the field, you can ignore this card's color requirements. [Main] <Draw 2>. Then, place this card in the battle area. [All Turns] When any of your level 5 or higher Digimon would leave the battle area, <Delay> • You may play 1 level 5 or lower Digimon card with the [ADVENTURE] trait from your hand without paying the cost. ---