Rulings
Q1: Can I use this card's Main effect to give "End of Your Turn Delete 1 of your Digimon" to a Digimon that isn't affected by effects?
You can give that effect to such Digimon, but Digimon that aren't affected by effects won't be affected by it. Therefore, "End of Your Turn Delete 1 of your Digimon" won't trigger at the end of that player’s turn for the Digimon that isn't affected by effects.
Q2: After this card's Main effect gives "End of Your Turn Delete 1 of your Digimon" to a Digimon, then that effect deletes a Digimon, does <Partition> on that Digimon trigger?
No, it doesn't trigger. After this card's Main effect gives "End of Your Turn Delete 1 of your Digimon" to a Digimon, then it triggers, that Digimon's player will be the player considered to have triggered/activated that effect, therefore <Partition> won't trigger.
Data Sources
Seventh Fascination EX7-072 R Seven Great Demon Lords [Trash] [Your Turn] When any of your Digimon digivolve into [Lilithmon (X Antibody)], by returning this card to the bottom of the deck, activate this card's [Main] effects. [Main] Until the end of your opponent's turn, give all of their Digimon "[End of Your Turn] Delete 1 of your Digimon." --- [Security] Delete 1 of your opponent's unsuspended Digimon.
Seventh Fascination EX7-072 R Seven Great Demon Lords [Trash] [Your Turn] When any of your Digimon digivolve into [Lilithmon (X Antibody)], by returning this card to the bottom of the deck, activate this card's [Main] effects. [Main] Until the end of your opponent's turn, give all of their Digimon "[End of Your Turn] Delete 1 of your Digimon." --- [Security] Delete 1 of your opponent's unsuspended Digimon.
Seventh Fascination EX7-072 R Seven Great Demon Lords [Trash] [Your Turn] When your Digimon digivolves into [Lilithmon (X Antibody)], by returning this card to the bottom of the deck, activate this card's [Main] effect. [Main] All your opponent's Digimon gain "[End of Your Turn] Delete 1 of your Digimon." until the end of their turn. --- [Security] Delete 1 of your opponent's unsuspended Digimon.
セブンス• ファシネイト EX7-072 R 七大魔王 [トラッシュ]【自分のターン】自分のデジモンが「リリスモンX抗体」に進化したとき、このカードをデッキの下に戻すことで、このカードの【メイン】効果を発揮する。 【メイン】相手のターン終了まで、相手のデジモン全てに「【自分のターン終了時】自分のデジモン1体を消滅させる。」の効果を与える。 --- 【セキュリティ】アクティブ状態の相手のデジモン1体を消滅させる。