

Q1: Can I activate the "when an effect trashes this card from the security stack" effect when this card is revealed from the security stack or when searching/looking at this card from the security stack?
No, you can't. You can only activate the "when an effect trashes this card from the security stack" when this card is directly trashed from the security stack.
Q2: Can I process the part of the effect after "then" in this card's Main effect without meeting the "by" condition?
No, you can't. If you don't trash your security card, you can't process the part after "then" in this card's Main effect.
Dragon's Roar BT18-098 C When this card is trashed from the security stack, activate its [Security] effects. While you have a yellow Digimon with the [Data] or [Witchelny] trait, you may ignore this card's color requirements. [Main] By trashing your top security card, 1 of your opponent's Digimon gets -6000 DP until the end of their turn. Then, if you have 2 or fewer security cards, place this card as your bottom security card. --- [Security] Delete 1 of your opponent's Digimon with 6000 DP or less. Then, if you have 0 security cards, <Recovery +1 ≪Deck≫>.
Dragon's Roar BT18-098 C When this card is trashed from the security stack, activate its [Security] effects. While you have a yellow Digimon with the [Data] or [Witchelny] trait, you may ignore this card's color requirements. [Main] By trashing your top security card, 1 of your opponent's Digimon gets -6000 DP until the end of their turn. Then, if you have 2 or fewer security cards, place this card as your bottom security card. --- [Security] Delete 1 of your opponent's Digimon with 6000 DP or less. Then, if you have 0 security cards, <Recovery +1 ≪Deck≫>.
Dragon's Roar BT18-098 C When this card is trashed from the security stack, activate its [Security] effects. While you have a yellow [Data] or [Witchelny] trait Digimon, you can ignore this card's color requirements. [Main] By trashing your top security card, 1 of your opponent's Digimon gets -6000 DP until the end of their turn. Then, if you have 2 or fewer security cards, place this card as your bottom security card. --- [Security] Delete 1 of your opponent's Digimon with 6000 DP or less. Then, if you have 0 security cards, <Recovery +1 (Deck)>.
ドラゴンズロア BT18-098 C このカードがセキュリティから破棄されたとき、このカードの【セキュリティ】効果を発揮する。 特徴に「データ種」/「ウィッチェルニー」を持つ黄の自分のデジモンがいる間、このカードは色条件を無視できる。 【メイン】自分のセキュリティを上から1枚破棄することで、相手のターン終了まで、相手のデジモン1体をDP-6000。その後、自分のセキュリティが2枚以下なら、このカードをセキュリティの下に置く。 --- 【セキュリティ】DP6000以下の相手のデジモン1体を消滅させる。その後、自分のセキュリティが0枚なら、≪リカバリー+1《デッキ》≫。