Do you have to live in the US to sign up for the beta of Hearthstone: Heroes of WarCraft

No, only you see your clicks and effects on the game board's 'environment'.

However, there are some opponent's actions that are visible to you, e.g: minions on the battlefield or hero powers are highlighted when your opponent hovers their mouse over them.

There are a few pieces of exclusive content thusfar in Hearthstone. The first is a golden 'Gelbin Mekkatorque' card, that could be earned by using real money to make a purchase in Hearthstone while it was in the beta.

The golden version of this card is no longer obtainable. It was previously obtained by spending real money in the store during the game's beta test, prior to the full release of the game.

In addition, golden 'Elite Tauren Chieftain' was only earnable through purchasing a ticket to Blizzcon 2013, and thus also can't be earned any longer.

However, the normal version of each of these cards are still both able to be earned through crafting them.

Card backs will likely be exclusive to each season and event, such as the ones earned through levels in ranked on specific seasons, but thusfar, I haven't seen anything specific about this yet.