Q1: If this card's Security effect reveals a black Digimon card with a play cost of 4 or less from the top of my deck, can I add it to the hand without playing it?
Yes, you can. This effect reads "you may play it without paying the cost," therefore you may choose to not play it. In such cases, because the effect reads "add the remaining cards to your hand," you add the card to your hand.
Lv.3 Dorumon P-070 P Rookie | Data | Beast/X Antibody [Security] At the end of the battle, reveal the top card of your deck. If it's a black Digimon card with a play cost of 4 or less, you may play it without paying its memory cost. Add the remaining cards to your hand. Then, add this card to its owner's hand.
Lv.3 Dorumon P-070 P Rookie | Data | Beast/X Antibody [Security] At the end of the battle, reveal the top card of your deck. If it's a black Digimon card with a play cost of 4 or less, you may play it without paying its memory cost. Add any remaining cards to your hand. Then, add this card to its owner's hand.
Lv.3 Dorumon P-070 P Rookie | Data | Beast/X Antibody [Security] At the end of the battle, reveal the top card of your deck. If that card is a {{Colour|black}} Digimon card with a play cost of 4 or less, you may play it without paying its memory cost. Add any remaining cards to your hand. Then, add this card to its owner's hand.
Lv.3 ドルモン P-070 P 成長期 | データ種 | 獣型/X抗体 【セキュリティ】バトル終了時、自分のデッキの上から1枚オープンする。そのカードが黒の登場コスト4以下のデジモンカードのとき、コストを支払わずに登場できる。残ったカードは手札に加える。その後、このカードを手札に加える。