The rate at which one currency can be purchased or sold is one of the terms of the option and is called the exercise price or strike price. American-style options can be exercised on any business day prior to the expiration date. European-style options can be exercised at expiration only. The same logic can be applied to currency pairs in which the U.S. dollar is not one of the currencies. Either currency can be expressed in terms of the other.
Intrinsic value is simply the difference between the spot price and the strike price.
A put option will have intrinsic value only when the spot price is below the strike price. A call option will have intrinsic value only when the spot price is above the strike price. Time value is more complex. When the price of a call or put option is greater than its intrinsic value, it is because it has time value. Time value falls toward zero as the expiration date approaches.