

Q1: What does "when an effect places the top card of one of your Digimon in a Digimon's digivolution cards" in this card's Your Turn effect mean, exactly?
You place the top card of one of your Digimon in the digivolution cards of that Digimon or another of your Digimon. This doesn't include when the top card becomes a digivolution card through digivolution.
Q2: I used this card's Start of Opponent's Turn effect to play and DNA digivolve a Digimon. In such cases, does the played Digimon's On Play effect activate?
No, it doesn’t. The On Play effect will trigger, but it can't activate because the Digimon becomes a digivolution card through DNA digivolution before the effect activates.
Sayo & Koh EX5-065 R Night Claw [Your Turn] When an effect places the top card of one of your Digimon in a Digimon's digivolution cards, by suspending this Tamer, gain 1 memory. [Start of Opponent's Turn] By playing 1 card with the same level as one of your [Night Claw] or [Light Fang] trait Digimon from that Digimon's digivolution cards without paying the cost, 2 of your Digimon may DNA digivolve into a Digimon card in your hand. At the end of the turn, return the Digimon played by this effect to the hand. --- [Security] Play this card without paying the cost.
Sayo & Koh EX5-065 R Night Claw [Your Turn] When an effect places the top card of one of your Digimon in a Digimon's digivolution cards, by suspending this Tamer, gain 1 memory. [Start of Opponent's Turn] By playing 1 card with the same level as one of your [Night Claw] or [Light Fang] trait Digimon from that Digimon's digivolution cards without paying the cost, 2 of your Digimon may DNA digivolve into a Digimon card in your hand. At the end of the turn, return the Digimon played by this effect to the hand. --- [Security] Play this card without paying the cost.
Sayo & Koh EX5-065 R Night Claw [Your Turn] When an effect places the top card of one of your Digimon in a Digimon's digivolution cards, by suspending this Tamer, gain 1 memory. [Start of Opponent's Turn] By playing 1 card with the same level as one of your [Night Claw] or [Light Fang] trait Digimon from that Digimon's digivolution cards without paying the cost, 2 of your Digimon may DNA digivolve into a Digimon card in your hand. At the end of the turn, return the Digimon played by this effect to the hand. --- [Security] Play this card without paying the cost.
サヨ&コウ EX5-065 R ナイトクロウ 【自分のターン】自分のデジモンに重ねられているカードが効果でデジモンの進化元に置かれたとき、このテイマーをレストさせることで、メモリー+1。 【相手のターン開始時】特徴に「ナイトクロウ」/「ライトファング」を持つ自分のデジモンの進化元から、そのデジモンと同じLv.のカード1枚をコストを支払わずに登場させることで、自分のデジモン2体で手札のデジモンカードにジョグレス進化できる。この効果で登場したデジモンはターン終了時に手札に戻る。 --- 【セキュリティ】このカードをコストを支払わずに登場させる。