Does this card's [All Turns] effect also give it the names from (Rule) on level 3 or lower cards in its digivolution cards?
Yes. "This Digimon gains all the names..." means that it also gains the names from (Rule) on digivolution cards.
Sep. 6, 2024
Does this card's [All Turns] effect also give it the names from Tamer cards and Option cards in its digivolution cards?
No, Tamer cards and Option cards don't have levels, therefore they don't meet the "level 3 or lower cards" condition and their names aren't gained.
Sep. 6, 2024
Can I use this card's [On Deletion] effect to hatch a Tamer card with [Tai Kamiya] in the breeding area?
No, you can't. "Hatch a Digi-Egg" means taking the top card of your Digi-Egg deck and placing it face-up in the breeding area.
Sep. 6, 2024