Q1: When effects play multiples of my Tokens and/or Digimon with the Puppet trait, can I use this card's Your Turn effect to give Rush to all of the played Digimon by suspending this Tamer?
No, you can't. You can only specify 1 Digimon that will gain Rush from among multiple Digimon that were played at the same time.
Arisa Kinosaki ST19-14 R LIBERATOR [Start of Your Turn] If you have 2 or less memory, set it to 3. [Your Turn] When effects play any of your Tokens or [Puppet] trait Digimon, by suspending this Tamer, 1 of those Digimon gains for the turn. (This Digimon can attack the turn it was played.) --- [Security] Play this card without paying the cost.
Arisa Kinosaki ST19-14 R LIBERATOR [Start of Your Turn] If you have 2 or less memory, set it to 3. [Your Turn] When effects play any of your Tokens or [Puppet] trait Digimon, by suspending this Tamer, 1 of those Digimon gains <Rush> for the turn. (This Digimon can attack the turn it was played.) --- [Security] Play this card without paying the cost.
Arisa Kinosaki ST19-14 R LIBERATOR [Start of Your Turn] If you have 2 or less memory, set it to 3. [Your Turn] When effects play one of your Tokens or a Digimon with the [Puppet] trait, by suspending this Tamer, 1 of those Digimon gains <Rush> for the turn. --- [Security] Play this card without paying the cost.
城之崎有紗 ST19-14 R リベレイター 【自分のターン開始時】メモリーが2以下なら、3にする。 【自分のターン】自分のトークンか特徴に「パペット型」を持つ自分のデジモンが効果で登場したとき、このテイマーをレストさせることで、ターン終了まで、そのデジモン1体は≪速攻≫(このデジモンは登場したターンでもアタックできる)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。