Q1: Can I use this card’s On Play effect to move a "Lv.-" Digimon from the breeding area to the battle area?
No, you can't. "Lv.-" Digimon and Digimon cards can't be targeted by effects that reference levels.
Q2: I moved a Digimon from the breeding area to the battle area when all of my Digimon's DP was reduced by activation of an effect. That Digimon's DP becomes 0 due to the DP-reducing effect at the same time it's moved to the battle area, then it's deleted, but does this card's Your Turn effect activate?
Yes, it activates.
Lui Ohwada P-130 P [On Play] You may move 1 of your level 3 or higher Digimon from the breeding area to the battle area. [Your Turn] When one of your Digimon moves from the breeding area to the battle area, by suspending this Tamer, gain 1 memory. --- [Security] Play this card without paying the cost.
Lui Ohwada P-130 P [On Play] You may move 1 of your level 3 or higher Digimon from the breeding area to the battle area. [Your Turn] When one of your Digimon moves from the breeding area to the battle area, by suspending this Tamer, gain 1 memory. --- [Security] Play this card without paying the cost.
Lui Ohwada P-130 P [On Play] You may move 1 of your level 3 or higher Digimon from the breeding area to the battle area. [Your Turn] When one of your Digimon moves from the breeding area to the battle area, by suspending this Tamer, gain 1 memory. ---
大和田ルイ P-130 P 【登場時】育成エリアのLv.3以上の自分のデジモン1体をバトルエリアに移動できる。 【自分のターン】自分のデジモンが育成エリアからバトルエリアに移動したとき、このテイマーをレストさせることで、メモリー+1。 --- 【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。