LED circuit with timer

Yes. Every point which is marked with a ground symbol should be connected to the negative terminal.

Yes.

The interval for which pin 3 is high is proportional to (R1+R2)*C and the interval for which pin 3 is low is proportional to R2*C. The cited values of R1=4k7, R2=150K, C=1uF result in on/off times of ~100ms (R1 is much less than R2, so R1+R2 is approximately equal to R2).

So, increasing the product R2*C by a factor of 20 will result in 2 second on/off times (i.e. a total period of 4 seconds). Pin 6 will draw up to 0.25uA, which (along with the leakage current of C) determines the upper limit of R1+R2.

Simply multiplying R2 by 20 would give 3MOhms; without any capacitor leakage, that would result in a constant 0.75V drop due to the current drawn by pin 6. The capacitor voltage oscillates between 1/3 and 2/3 of Vcc, i.e. 2-4V for a 6V supply. A 0.75 drop would be enough to make the output noticably asymmetric, i.e. one group of LEDs would be on for noticably longer than the other.

Also, at such long periods, capacitor leakage current is likely to be a major factor with an electrolytic capacitor. My instinct says change C1 to a 10uF tantalum electrolytic and R2 to 330K. That gives ~18uA charge/discharge current, which is significantly above the currents sourced/sunk by pins 2 and 6 and typical capacitor leakage (note that a normal aluminium electrolytic could easily leak the entire 18uA, so that isn't an option).

If you want a higher resistance and a smaller capacitance, you'll probably need to abandon electrolytics in favour of e.g. polyester, which will have a significantly lower leakage at the expense of a larger package and higher cost (Farnell quotes £0.17 for a 10uF tantalum vs £1.20 for a

OTOH, for a one-off, you may as well ignore the cost and just go with C = 10uF poly, R2 = 330K. That will allow you to treat both the capacitor and 555 as "ideal" (i.e. you can ignore currents other than the actual charge/discharge current).

Use a variable resistor for R2.

Both Signetics and National Semiconductor published application notes (in the 70's) that tell you how a 555 works, and some ways to use it (along with nomographs) allowing you to chose resistor/capacitor combinations for various delays/frequencies.

There are several good explanations on the web also if you can't find the original application notes.

The 555 is easy to understand and would be an excellent place to further your electronics learning. Understand what is inside, and you'll be much more able to apply it - and it is interesting stuff.

Beyond that, will one single 555 sink or source enough current to light 20 leds simultaneously? Depends on how much current the leds draw and how much power supply voltage you have, and which variant of the 555 you have, how bright you want them to be, what the ambient temperature is and how long you expect them to last.

Contrary to popular belief, Leds do not last forever. They have a half-life - half the brightness over a specific time period influenced by how hot the die gets.