Rulings
Q1: If I activate an effect that reduces the cost of an Option card with a cost of 2 or more and I only pay a cost of 1, or if I do not pay the cost at all by activating an effect that allows me to use an Option card without paying the cost, does this card's inherited effect activate?
Yes, as long as the Option card you use has a cost of 2 or more, this card's inherited effect activates regardless of the actual cost paid.
Q2: Does this card's inherited effect activate if I use an Option card when it has a cost of 1 or less due to a "reduce the cost of this card in the hand by 1" effect on a card such as such as BT2-099 Glorious Burst or BT8-097 Crimson Blaze?
No, it doesn’t activate. It doesn't activate if the cost of an Option card consistently changes when it's in the hand and becomes 1 or less due to that card's effect.
Data Sources
Lv.4 Kyubimon BT17-032 C Champion | Data | Mysterious Beast [When Digivolving] If you don't have [Rika Nonaka], you may play 1 [Rika Nonaka] from your hand without paying the cost. --- Inherited: [Your Turn] [Once Per Turn] When you use an Option card with a cost of 2 or more, 1 of your opponent's Digimon gains <Security A. -1> until the end of their turn.
Lv.4 Kyubimon BT17-032 C Champion | Data | Mysterious Beast [When Digivolving] If you don't have [Rika Nonaka], you may play 1 [Rika Nonaka] from your hand without paying the cost. --- Inherited: [Your Turn] [Once Per Turn] When you use an Option card with a cost of 2 or more, 1 of your opponent's Digimon gains <Security A. -1> until the end of their turn.
Lv.4 Kyubimon BT17-032 C Champion | Data | Mysterious Beast [When Digivolving] If you don't have [Rika Nonaka], you may play 1 [Rika Nonaka] from your hand without paying the cost. --- Inherited: [Your Turn] [Once Per Turn] When you use an option card with a cost of 2 or more, 1 of your opponent's Digimon gains <Security A. -1> until the end of their turn.
Lv.4 キュウビモン BT17-032 C 成熟期 | データ種 | 妖獣型 【進化時】自分の「牧野留姫」がいないなら、自分の手札から、「牧野留姫」1枚をコストを支払わずに登場できる。 --- Inherited: 【自分のターン】[ターンに1回]自分が使用コスト2以上のオプションカードを使用したとき、相手のターン終了まで、相手のデジモン1体に≪Sアタック-1≫を与える。