Q1: What does a card with "X in its text" refer to?

It refers to a card that contains the specified text or icon in its name, traits, effects, inherited effects, (Rule), digivolution requirements, DNA digivolution, DigiXros requirements, burst digivolve, App Fusion, Link, or Assembly requirements. For example, a card with Knightmon in its text would include cards with the name DarkKnightmon and cards with the text Knightmon in their effects.

Q2: 2 copies of this card are in the battle area. Can I activate the Main effect on both copies of this card and play or use 1 of the specified cards with the cost reduced by the total value?

No, you can't. You can't activate multiple effects that play or use a card at the same time.

Q3: If I activate this card's Main effect while a Digimon such as ST12-03 Solarmon with a "players can't reduce play costs" effect is in the battle area, can I activate this card's Main effect and play 1 of the specified cards?

You can activate the effect and play such a card, but its play cost won't be reduced.

Q4: If I activate this card's Main effect while a Digimon such as BT9-047 Pomumon with a "players can't play Digimon by effects" effect is in the battle area, can I activate this card's Main effect and play 1 of the specified cards?

You can activate the effect, but you can't use it to play such a card.