Q1: Can I use this card's On Play When Digivolving effect to place a BT11-063 Geremon or BT15-035 Geremon from my trash in this card's digivolution cards?
Yes, you can. BT11-063 Geremon and BT15-035 Geremon have a rule that also treats them as having the name Numemon, therefore you can place them as digivolution cards under this Digimon.
Lv.6 ShinMonzaemon ST19-13 U Mega | Vaccine | Puppet [Digivolve] Lv.5 w/[Monzaemon]/[Numemon] in name: Cost 3 <Armor Purge> (When this Digimon would be deleted, by trashing this Digimon's top stacked card, it isn't deleted.) [On Play] [When Digivolving] By placing 1 level 5 or lower card with [Numemon] in its name or the [Puppet] trait from your trash as this Digimon's bottom digivolution card, <Recovery +1 (Deck)>. (Place the top card of your deck as your top security card.)
Lv.6 ShinMonzaemon ST19-13 U Mega | Vaccine | Puppet [Digivolve] Lv.5 w/[Monzaemon]/[Numemon] in name: Cost 3 <Armor Purge> (When this Digimon would be deleted, by trashing this Digimon's top stacked card, it isn't deleted.) [On Play] [When Digivolving] By placing 1 level 5 or lower card with [Numemon] in its name or the [Puppet] trait from your trash as this Digimon's bottom digivolution card, <Recovery +1 (Deck)>. (Place the top card of your deck as your top security card.)
Lv.6 ShinMonzaemon ST19-13 U Mega | Vaccine | Puppet [Digivolve] Lv.5 w/[Monzaemon]/[Numemon] in name: Cost 3 <Armor Purge> [On Play] [When Digivolving] By placing 1 level 5 or lower card with [Puppet] trait or with [Numemon] in its name from your trash as this Digimon's bottom digivolution card, <Recovery +1 (Deck)>.
Lv.6 しんもんざえモン ST19-13 U 究極体 | ワクチン種 | パペット型 名称に「もんざえモン」/「ヌメモン」を含むLv.5:コスト3 ≪アーマー解除≫(このデジモンが消滅するとき、このデジモンに重ねられているカードを上から1枚破棄することで、消滅しない) 【登場時】【進化時】自分のトラッシュから、名称に「ヌメモン」を含むか特徴に「パペット型」を持つLv.5以下のカード1枚をこのデジモンの進化元の下に置くことで、≪リカバリー+1《デッキ》≫(自分のデッキの上から1枚をセキュリティの上に置く)。