Yeah, with something like an amp, you have to look as the capacitor's AC-passing (impedance) abilities instead.
The theory for oscillators is generally the same as we discussed on RC and RL circuits. Timing is done by repeatedly chargine & discharging the capacitor and triggering the output when the capacitor voltage reaches some arbitrary point. The same could be said for inductors, except they have an ability to interfere with each other magnetically, so they are less common. In short, it's all about exponential decay.
The time period for an oscillator is whatever you design it to be. I imagine the 555 timer used the 33% and 66% voltages for easy calculations.
In fairness, not all oscillators use the RC/RL decay. They're just highly popular because of thier low cost, wide availability, and small space; versus crystal oscillators which are higher cost, lower availability, and higher accuracy. You can also mix-and match R's and C's or use variable ones to "tweak" it to frequencies you can't easily get with fixed crystals. It's a matter of trade-offs.