555 timer output current

I suspect that they use a 9 volt battery since it is a handy, readily-available power source.

The electrical characteristics of LEDs (and diodes in general) are a bit odd - they don't follow Ohm's Law. The voltage across an ordinary ("bare") LED depends primarily on its colour, and will vary only slightly with current (for a red LED, the voltage will be about 1.8 volts). Therefore it is necessary to include something in an LED circuit to limit the current to a safe value - the 1K resistor in the circuit you linked to serves as the currrent limiter.

An LED advertised as "12 volts" or "5 volts" will include a series resistor or other current-limiting device, and can be connected directly to the advertised voltage with no other components.

A "bare" red LED will have a voltage drop of about 1.8 volts, yellow is about 2 volts, and green is about 2.2 volts. Blue and white are about 3.3 volts (white LEDs are really blue LEDs with a yellow phosphor).

As Nasha has already pointed out, using a CMOS 555 will greatly cut down on the quiescent current required from the battery, as well as eliminate the huge shoot-through current spikes inherent in the bipolar 555's output totem-pole every time it switches.

Another area of concern is the timing capacitor's chemistry and capacitance.

In order to minimize its own leakage, the cap should be something other than electrolytic, (plastic or ceramic dielectric, say,) and its capacitance should be selected to be as small as possible and, in the circuit you've linked to, the value of the resistors should be made as large as possible since every time the cap charges and discharges all that energy is just wasted.

Also, C2 can be eliminated.