EF can certainly be confusing; it provides a lot of information, which is terrifically value if one knows how to use it, but can be bewildering otherwise. In brief, EF provides access to data that travel agents have (it of course only provides access to the data, meaning the ability to view it). I use EF more for finding good routes and desirable flights than for finding fares, but I do sometimes use it to find fares.

The Fare Information query, by default, shows fares available between the cities you specify on the dates you specify. Note that it only shows the base fares, not the fares with airline-imposed surcharges and government taxes and fees. By default, it only shows fares for which there is also availability on flights on your dates. Since the fares shown by default are available and have corresponding flights available, you should be able to book those flights and get that fare through an airline or online travel agency. So why look at EF? If you use some of the non-default settings, you can empower yourself to find lower fares. For example, if you check the box that says "Show fares for all dates" and uncheck the box that says "Validate fares," you will see fares that are available between your cities but perhaps not on the exact dates you entered or for which flights on those days don't have the correct inventory. What's the use of that? You can see potentially much lower fares. If you examine the fare rules (available by clicking a button on the fare), it might be a bit tedious to read, but you'll see if there are date or day of week restrictions, which airlines can be used, required booking inventory, advance purchase, minimum stay, and other limitations. Armed with that detailed information, you can work backwards to obtain that fare. Perhaps you need to adjust your outbound or inbound dates. Perhaps you need to use the Flight Availability query to find flights with the needed inventory. Maybe the fare allows free stopovers at certain points? You can take advantage of that.

Exactly.