Q1: Does this card's Your Turn effect trigger when my Digimon is played by <Partition>?
Yes, it triggers. It triggers because <Partition> is an effect where the specified cards are played from digivolution cards.
Minami Uehara BT17-082 U [On Play] You may play 1 [Labramon] or [Seasarmon] from your hand or one of your Digimon's digivolution cards without paying the cost. [Your Turn] When one of your Digimon is played from digivolution cards, by suspending this Tamer, 1 of your blue Digimon gains <Rush> for the turn. --- [Security] Play this card without paying the cost.
Minami Uehara BT17-082 U [On Play] You may play 1 [Labramon] or [Seasarmon] from your hand or one of your Digimon's digivolution cards without paying the cost. [Your Turn] When one of your Digimon is played from digivolution cards, by suspending this Tamer, 1 of your blue Digimon gains <Rush> for the turn. --- [Security] Play this card without paying the cost.
Minami Uehara BT17-082 U [On Play] You may play 1 [Labramon] or [Seasarmon] from your hand or from one of your Digimon's digivolution cards without paying the cost. [Your Turn] When one of your Digimon is played from digivolution cards, by suspending this Tamer, 1 of your blue Digimon gains <Rush> for the turn. --- [Security] Play this card without paying the cost.
上原美波 BT17-082 U 【登場時】自分の手札か自分のデジモンの進化元から、「ラブラモン」/「シーサモン」1枚をコストを支払わずに登場できる。 【自分のターン】進化元から自分のデジモンが登場したとき、このテイマーをレストさせることで、ターン終了まで、青の自分のデジモン1体は≪速攻≫を得る。 --- 【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。