

Q1: If I use this card's On Deletion effect to return this card to the hand, does it mean that this card isn't sent to the trash?
No, an On Deletion effect activates after the card is moved to the trash. Therefore, the card is first sent to the trash.
Q2: I have Sukamon A and Sukamon B with this card in their digivolution cards in the battle area. When Sukamon A would be deleted, I attempted to delete Sukamon B using this card's inherited effect. On the other hand, when Sukamon B would be deleted, I attempted to delete Sukamon A using this card's inherited effect. At such times, can Sukamon A activate this card's inherited effect again?
No, it can't be activated. Until the processing for the 1st activation has resolved, only 1 activation is possible for each immediate-type effect. In your case, until the deletion of the 1st only Sukamon A is resolved, only 1 activation is possible for each "when ... would" effect, therefore the effect that has already activated for Sukamon A can't be activated again.
Lv.4 Targetmon EX5-046 U Champion | Virus | Puppet <Blocker> [On Deletion] By trashing 1 card with [Etemon] or [Sukamon] in its name in your hand, return this card to the hand. (Rule) Name: Also treated as having [Etemon] and [Sukamon]. --- [All Turns] When this Digimon would be deleted, by deleting 1 other Digimon with [Sukamon] in its name, prevent that deletion.
Lv.4 Targetmon EX5-046 U Champion | Virus | Puppet <Blocker> [On Deletion] By trashing 1 card with [Etemon] or [Sukamon] in its name in your hand, return this card to the hand. (Rule) Name: Also treated as having [Etemon] and [Sukamon]. --- [All Turns] When this Digimon would be deleted, by deleting 1 other Digimon with [Sukamon] in its name, prevent that deletion.
Lv.4 Targetmon EX5-046 U champion | Virus | Puppet <Blocker> [On Deletion] By trashing 1 card with [Etemon] or [Sukamon] in its name in your hand, return this card to the hand. (Rule) Name: Also treated as having [Etemon] and [Sukamon]. --- [All Turns] When this Digimon would be deleted, by deleting 1 other Digimon with [Sukamon] in its name, prevent that deletion.
Lv.4 ターゲットモン EX5-046 U 成熟期 | ウィルス種 | パペット型 ≪ブロッカー≫ 【消滅時】自分の手札から、名称に「エテモン」/「スカモン」を含むカード1枚を破棄することで、このカードを手札に戻す。 〈ルール〉名称:「エテモン」/「スカモン」を含むものとしても扱う。 --- 【お互いのターン】このデジモンが消滅するとき、名称に「スカモン」を含む他のデジモン1体を消滅させることで、消滅しない。