The first question is difficult. The rulebook states that "a model in a scoring unit can seize the Relic... From that point, the Relic remains with the model until it is dropped, which can happen voluntarily, but happens automatically if the model is slain or falls back." and it also says "a model carrying the Relic can transfer it to any friendly model that is part of a scoring unit if the two models end their movement phase in base contact." I would interpret that as the independent character would have to be in a scoring unit to seize or receive the Relic however from that point on it remains with him, even if he moves off and joins another unit. It only states you need to be a model in a scoring unit to pick it up but it doesn't place any constraints on then moving him about. He would only drop it if he falls back or dies. However that could be interpreted in many ways so it's anything but set in stone.
The second question seems easier but is still very valid. The rulebook says "at the end of the game, the Relic is worth 3 victory points to the player who has seized it." This could be interpreted as as 3 victory points every time it's seized however it seems to indicate that only one player can do this and also because if the theme of the overall mission, I would take seized to mean control or holds. When you think about it, what's the point of giving the win to the person who doesn't even hold the object your fighting for? After all, the entire mission is about taking a valuable item so there really would be no point giving victory person who failed to keep the item. Therefore I would take it as whichever player has the model with the Relic attached to him when the game ends gets the points.
Darkness falls across the land, the midnight hour is close at hand, creatures crawl in search of blood, to terrorize y'alls neighbourhood.
And whosoever shall be found, without the soul for getting down, must stand and face the hounds of hell, and rot inside a corpse's shell.