I've used this website to figure out how to wire up an LED project I am going to do, the only thing I'm not convinced by is the fact that on this diagram they have supplied me the resistors are after the LEDs. Is this correct, is this wrong, or am I just reading it wrong. I am reading it as I have 3 parallel sets of 4 LEDs in series with the resistors on the negative end of each set.
Current is the same for all nodes in a series circuit. As such, you can put the resistor anywhere in that series string. Each of those 3 parallel sets is a series circuit.
As to your other question, the leds will fade over the 4 hours, not just after the 4th hour, as the 9v battery is being drained. Since you are drawing 60mA, it will drain faster than the 4 hours you see.
The resistors are shown in series with the LEDs. It doesn't matter what order the four LEDs and the resistor of each LED string are connected in. You can scramble them any way you want, as long as they stay in series, and you will get the same result.
One way to convince yourself of this is to realize the current is the same for all devices connected in series. Since the same current goes thru the resistor no matter where you place it in the series string, it drops the same voltage. That leaves the same remaining voltage for the LEDs, again regardless of order.