A plane card is treated as if its text box included "When you roll {PW}, put this card on the bottom of its owner's planar deck face down, then move the top card of your planar deck off that planar deck and turn it face up." This is called the "planeswalking ability."

A face-up plane card that's turned face down becomes a new object with no relation to its previous existence. In particular, it loses all counters it may have had.

The controller of a face-up plane card is the player designated as the "planar controller." Normally, the planar controller is whoever the active player is. However, if the current planar controller would leave the game, instead the next player in turn order that wouldn't leave the game becomes the planar controller, then the old planar controller leaves the game. The new planar controller retains that designation until they leave the game or a different player becomes the active player, whichever comes first.

If an ability of a plane refers to "you," it's referring to whoever the plane's controller is at the time, not to the player that started the game with that plane card in their deck. Many abilities of plane cards affect all players, while many others affect only the planar controller, so read each ability carefully.

If multiple creatures deal combat damage to a player, the first ability of Undercity Reaches triggers multiple times.

If a creature deals combat damage to a player, the controller of Undercity Reaches controls the ability that triggers, but the controller of the creature decides whether to draw a card.

The chaos ability's effect continues to apply even after Undercity Reaches stops being the face-up plane card.

If multiple effects modify your hand size, apply them in timestamp order. For example, if you put Null Profusion (an enchantment that says your maximum hand size is two) onto the battlefield and then roll {CHAOS} while Undercity Reaches is the face-up plane card, you'll have no maximum hand size. However, if those events had happened in the opposite order, your maximum hand size would be two for as long as Null Profusion is on the battlefield.