American options can be exercised at any time between the date of purchase and the expiration date. European options are different from American options in that they can only be exercised at the end of their lives on their expiration date. The distinction between American and European options has nothing to do with geography, only with early exercise. Many options on stock indexes are of the European type. Because the right to exercise early has some value, an American option typically carries a higher premium than an otherwise identical European option. This is because the early exercise feature is desirable and commands a premium.
With straddles (long in this example), you as a trader are expecting the asset (like a stock) to be highly volatile, but don't know the direction in which it will go (up or down). When using a straddle strategy, you as the trader are buying a call and put option at the same strike price, underlying price and expiry date. This strategy is often used when a trader is expecting the stock of a particular company to plummet or skyrocket, usually following an event like an earnings report. For example, when a company like Apple (AAPL) is getting ready to release their third quarter earnings on July 31st, an options trader could use a straddle strategy to buy a call option to expire on that date at the current Apple stock price, and also buy a put option to expire on the same day for the same price.
An option's price, its premium, tracks the price of its underlying futures contract which, in turn, tracks the price of the underlying cash. Therefore, the March T-bond option premium tracks the March T-bond futures price. The December S&P 500 index option follows the December S&P 500 index futures. The May soybean option tracks the May soybean futures contract. Because option prices track futures prices, speculators can use them to take advantage of price changes in the underlying commodity, and hedgers can protect their cash positions with them. Speculators can take outright positions in options. Options can also be used in hedging strategies with futures and cash positions.
The price at which you agree to buy the underlying security via the option is called the "strike price," and the fee you pay for buying that option contract is called the "premium." When determining the strike price, you are betting that the asset (typically a stock) will go up or down in price. The price you are paying for that bet is the premium, which is a percentage of the value of that asset.