Each Clan should initially have a few relics. But later, they will naturally be passed from one Clan to another as a result of Clan Wars. However, one relic is too few, in my opinion. In this case, the functionality of the artifact idea would hardly differ from the territory idea. Theoretically, you could create a set for each Clan (as has already been suggested), but if the artifacts are distributed randomly, one of the main goals of the Clans will be to collect their own set. Although, that might be too much. But still, each year, the results will be summarized: which Clans managed to collect a set, which Clans have the most artifacts in general, etc. And to prevent someone from trying to collect someone else's set, one artifact from their own set must never be lost under any circumstances.
Yes, practically everything is correct.
It's not necessary to have one artifact per Clan; you could have one relic that each Clan creates, and parts of several sets – neutral ones – distributed randomly.
But I don't see the point in having an artifact that cannot be taken; I already wrote that the conditions for capturing it should be very easy.
It's even hard to imagine the situation at the moment when the strongest player of one Clan can lose to the weakest player of another Clan. What kind of Clan would that be?
By the way, Clans don't participate in such Clan Wars analytically; something else, an alternative, can be devised for them