Arcgain's [Constant] ability does not prevent Lancer, because Lancer affects the opponent's Life Cloth, not the SIGNI themselves.
Arcgain's [Constant] ability does not protect against abilities that change how the rules work, such as the [Action] ability of Energe, Original Spear.
Arcgain's [Constant] ability protects against your opponent's abilities that cause the player with Arcgain to make a choice, such as the [Constant] ability of Anna Mirage, Devil Princess or Self Slash, because those are still considered to be the opponent's abilities. In these cases, the player with Arcgain on the field is not forced to choose a SIGNI that can be affected by those abilities. Instead, they can choose one of their <Angel> SIGNI for the ability, and those abilities will resolve without affecting their <Angel> SIGNI.
Abilities which will otherwise affect your <Angel> SIGNI if Arcgain were not present on the field do not apply retroactively even if Arcgain leaves the battlefield after the effect is resolved. For example, if the opponent uses the third ability of Ancient Surprise, your <Angel> SIGNI do not lose power even when Arcgain leaves the battlefield after Ancient Surprise has finished resolving.
Even if you have Arcgain on the field, the abilities of your opponent's cards can still add Charms to Arcgain and your other <Angel> SIGNI. Adding a Charm is not treated as affecting a SIGNI.