Hi Julian
I will like to answer your doubts in order they have been asked:-
1.Yes you can use two 6V panels instead of single 12V panel. You should connect these two 6V solar panles in series in order to get 12V.
2.If you want 5V output from circuit, it is better to use a solar panel which can provide voltage greater than 5V. This wil help the circuit to perform well enough. Now here's a basic thing related to batteries or voltage sources; when you connect them in parallel you tend to increase their current capacity and when you connect them in series their voltage increases. So if you want a better power source, with same voltage rating, you should connect solar panels in parallel. I hope this clears your current and power relation doubt.
3.Yes you can use normal rechargeable batteries as well, just make sure these batteries do meet the current and voltage requirements of the circuit.