Needing clarification on capacitors

[Redcap]

I'm very new to electronics and was hoping someone would be to shed some light on the questions I have regarding Caps.

As I understand it, the V rating on the capacitor indicates the maximum volts that can be applied to it before probable failure.
When a Cap is set up with a trigger system to dump (X) amount of stored energy [or rather dump stored energy when it reaches (X)], (X) can be set to anything less than or equal to the max voltage rating, as the max voltage rating is also the maximum the Cap can potentially store.

Is that correct..?  

If so, does applying a power source less than the Cap's max voltage rating allow it to store volts until its max [eg, will a power source of 9v over enough time, allow a 16v cap to build up voltage to 16v], or only that equal to the power source?

[waltr]

Only to the voltage of the power source. If you charge a cap with a 9V battery the voltage on the cap will only reach 9V.
The voltage rating is the MAX voltage before the cap fails, sometime spectacularly.
If you have a circuit such as the 5V regulator output, you can use any cap with a Max voltage rating greater than the circuit voltage. For a 5V circuit the minimum cap voltage rating I would use is 6.3V but would prefer a higher rating like 10V.

Read up on "RC circuits" and then experiment. You only need a voltmeter (multimeter) some resistors and caps.

[Redcap]

Thank you very much, Waltr