Two questions here first can Caster's Champion users benefit from the gloves at all?
Second do I have to be under the effects of Arcane Strike/Caster's Champion for the bonuses to take effect?
Requirement: Only a spellcaster with the Arcane Strike feat can activate the abilities of these gloves.
These abilities are as follows:
When the wearer uses the aid another action to improve an ally’s attack roll, the ally adds the wearer’s Arcane Strike damage bonus to its damage roll for that attack.
When the wearer makes an attack using Arcane Strike and hits, enemies adjacent to the target take damage equal to the wearer’s Arcane Strike damage bonus. This damage is of the same type as the weapon’s damage (bludgeoning, piercing, and so on).
When the wearer uses the aid another action to improve an ally’s Armor Class, the ally also adds the wearer’s Arcane Strike damage bonus to his AC against the opponent.
Special: This feat counts as Arcane Strike for the purposes of prerequisites.
1. No. While Caster's Champion counts as Arcane Strike for the purpose of prerequisites, it does not count as Arcane Strike for any other purpose. So the gloves would be usable, but there'd be no Arcane Strike bonus damage to add.
2. No, you do not have to activate Arcane Strike to use the gloves. They just work.
1. RAW - No (as Blaphers said), but it looks more like an oversight than a deliberate choice. I'd probably let it work. So RAW - no, but RAI - maybe?
2. For the two Aid-Another actions it doesn't specifically say you have to activate Arcane Strike. I could see the reasoning that you do, but I think RAW Blaphers is right (I'd check with my GM first).
For the bonus damage option you'd have to use Arcane Strike.