Q1: When an effect plays an opponent's Digimon into the breeding area, does this card's All Turns effect activate?
No, it doesn't activate.
Q2: Does this card's All Turns effect also activate when one of my effects plays an opponent's Digimon/Tamer?
Yes, it activates.
Q3: Can I use this card's When Digivolving effect to delete just 1 of my opponent's Digimon if my opponent has level 3, level 5, and level 7 Digimon?
No, you can't. You must delete as many as possible.
Q5: My EX5-063 Leviamon with Security Attack +1 attacked a player, and a Digimon or Tamer was played by a Security effect upon the 2nd security check. This caused the EX5-063 Leviamon to digivolve into this card from the trash. This card has Security Attack +2, but does it get 2 additional security checks?
No, it only gets 1 additional security check. EX5-063 Leviamon's Security Attack +1 is lost upon the digivolution but it gains Security Attack +2, so the total possible security checks will be 3. In the situation from your question, you have already performed 2 security checks, so you have 1 security check remaining.
Q6: I have this card and Leviamon in my trash, then my [EX5-069 Biting Crush was placed in the battle area. If my opponent's Digimon is played by an effect at this time, this card and EX5-069 Biting Crush will trigger simultaneously, but can I activate EX5-069 Biting Crush's effect first to play Leviamon from my trash and then use the effect to digivolve that Leviamon into this card?
Yes, you can.
Lv.6 Leviamon (X Antibody) BT15-081 SR Mega | Virus | Demon Lord/Seven Great Demon Lords/X Antibody [Digivolve] [Leviamon]: Cost 2 [Trash] [All Turns] When an effect plays an opponent's Digimon or Tamer, 1 of your [Leviamon] or Digimon with [X Antibody] in their digivolution cards may digivolve into this card without paying the cost. <Security A. +2> [When Digivolving] If your opponent has as many or more total Digimon and Tamers as you, delete 1 of their Tamers. Then, delete 1 of your opponent's level 3, 1 of their level 5 and 1 of their level 7 Digimon. --- Inherited: -
Lv.6 Leviamon (X Antibody) BT15-081 SR Mega | Virus | Demon Lord/Seven Great Demon Lords/X Antibody [Digivolve] [Leviamon]: Cost 2 [Trash] [All Turns] When an effect plays an opponent's Digimon or Tamer, 1 of your [Leviamon] or Digimon with [X Antibody] in their digivolution cards may digivolve into this card without paying the cost. <Security A. +2> [When Digivolving] If your opponent has as many or more total Digimon and Tamers as you, delete 1 of their Tamers. Then, delete 1 of your opponent's level 3, 1 of their level 5 and 1 of their level 7 Digimon. --- Inherited: -
Lv.6 Leviamon (X Antibody) BT15-081 SR mega | Virus | Demon Lord/Seven Great Demon Lords/X Antibody {{DigivolveFromNames|2|Leviamon}} [Trash] [All Turns] When an effect plays an opponent's Digimon or Tamer, 1 of your [Leviamon] or Digimon with [X Antibody] in their digivolution cards may digivolve into this card without paying the cost. <Security A. +2> [When Digivolving] If your opponent has as many or more total Digimon and Tamers as you, delete 1 of their Tamers. Then, delete 1 of your opponent's level 3, 1 of their level 5 and 1 of their level 7 Digimon.
Lv.6 リヴァイアモンX抗体 BT15-081 SR 究極体 | ウィルス種 | 魔王型/七大魔王/X抗体 [トラッシュ]【お互いのターン】効果で相手のデジモン/テイマーが登場したとき、自分の「リヴァイアモン」か進化元に「X抗体」がある自分のデジモン1体をこのカードにコストを支払わずに進化できる。 ≪Sアタック+2≫ 【進化時】相手のデジモンとテイマーの合計体数が自分のデジモンとテイマーの合計体数以上なら、相手のテイマー1体を消滅させる。その後、Lv.3とLv.5とLv.7の相手のデジモン1体ずつを消滅させる。 --- Inherited: undefined