A few comments on that dual 555 schematic:
- instead of two 555s you can also use a 556.
- C1 and C2 should be film capacitors, much better stability when it comes to timing. This person used an electrolytic for C1 and 3x ceramic for C2. Especially ceramics give quite unstable results.
- C2 can be replaced by a single 330 nF cap. No need to have three in parallel. That's probably because of what he happened to have on hand (just like that 2.2µ electrolytic).
- that 0.68µ cap can indeed be necessary; a bigger value will work fine as well. It's for power supply decoupling. Better would be to use one larger electrolytic and a smaller ceramic in parallel (e.g. 10µF and 100 nF).