Capacitors can be used to store energy, but their capability to store energy opens up doors for other functions. Capacitors can be used to stabilize circuits, be used for timing, for feedback phase shift, etc.
Resistors do consume some energy, because of released heat. Besides that, resistors mainly limit the amount of current (the number of electrons flowing). If too much current is allowed to flow, then this can harm electronic components or generate heat.
Any voltage regulator will work, as long as that regulator can handle the amount of current flowing through it. Before you buy a regulator, look at the reviews, they tell you if the regulator is good quality or not.
This solar panel should work. Mobile devices pull only as much current as they need. This means you should not have to worry about frying your phone. Just make sure that the voltage that your circuit is giving you phone is the correct amount. Most phones take 5V to charge. Your voltage regulator needs to be a 5V regulator. I believe your regulator is 5V.
By mah, I believe you are talking about Mili-Amp Hours. This is simply a method of measuring how much a battery can store. If you have a 5000mAh battery, this means that this battery can give 5000 Mili-Amps for an Hour before the battery dies. Mili-Amps is a measurement for current.
I recommend that you look into Ohms law, which is V=IR (V is voltage, I is current, and R is resistance). That will explain to you how Voltage, Current, and Resistance are all related. You can think of voltage as electrical pressure. Current is the amount of electrons that are flowing. Resistance is trying to stop the current. The voltage pushes the current, and resistance tries to stop the current.
Hope this helps.