Brush

What happens when you conquer Aspirant's Climb with Green Father and Brush the battlefield when both players are at 8 points?

If this is the first battlefield that player has scored, they'll draw 1 and the game will continue with both players at 8 points.

If you replace Aspirant's Climb with Brush via Green Father's conquer or hold effect, the Victory Score will change immediately as the passive ability of Aspirant's Climb is no longer in effect, bringing both players to the Victory Score simultaneously. Rules 323.1. and 467. define winning the game as happening during a cleanup when one player has points greater than or equal to the Victory Score and greater than any opponent. If both players are at 8 points, they have not fulfilled both requirements for winning the game. They will need to score additional points in order to win. When they do so, 466.1.b. says "when a player tries to gain a point through a Score, and their current point total is one point from the Victory Score for their Mode of Play or higher, do the following: ..." If the point is from Conquering, they will draw 1 instead of gaining the point unless they have scored each battlefield that turn. In effect, every point at or above the Victory Score becomes the final point.

323.1.1. If a player has points greater than or equal to the Victory Score, and more points than any opponent, that player wins.467.When a cleanup occurs and a player has accrued Points greater than or equal to the Victory Score for their Mode of Play, and if they have more points than any opponent, they Win the Game.

What happens if you Brush a Brush? Can you swap back the original battlefield you Brushed?

The Brush token will cease to exist. When swapping back, a player can choose to swap back to any object that was replaced, including the original battlefield.

This is because a replacing game object inherits all of the statuses and conditions of the game object it replaced, per 438.1. A game object can be instructed to "swap back"; the token stops existing and the original card is returned to the space that the token occupied, inheriting all its current effects and statuses per rule 438.7.b. "All of the effects and statuses" includes not only temporary effects applied to the battlefield, but also the relationship between replaced and replacing battlefields.

438.1.Replacing is the act of Creating a token in the place of another card or token without playing it while inheriting all effects or statuses of the game object it replaced.438.7.b.To Swap Back, the token stops existing and the original card is returned to the space that the token just occupied, inheriting all current effects and statuses.

187.8. A Brush battlefield token is a domainless battlefield token with "Bird, Cat, Dog, Poro, and Ivern units here have +1 [M]" and "When you score here, you may replace this with the battlefield it replaced."

438.1.a. The replacing token is treated as the same Game Object as the card or token it replaced for the purposes of Game Effects that target or reference that game object. Example: A player with Green Father as their legend conquers Navori Fighting Pit. They choose to place the Green Father conquer effect on the chain after the Navori Fighting Pit conquer effect. When the Green Father trigger resolves, Navori Fighting Pit is replaced with Brush. Although the Navori Fighting Pit has been replaced, the "here" in its triggered ability still can have its information referenced, because the Brush inherited all statuses and conditions. The unit Navori Fighting Pit's triggered ability has targeted will still be a legal target on resolution.