Series and parallel
Batteries in series add their voltages at the same capacity: two 12 V 100 Ah batteries make 24 V 100 Ah. In parallel, the capacity adds at the same voltage: 12 V 200 Ah. Either way the stored energy, in watt-hours, doubles. Only combine batteries of the same type, age and capacity, and use a battery management system with lithium cells.
Usable capacity
Lead-acid batteries last far longer if you use only about half their capacity before recharging. LiFePO4 batteries can use 80 to 90%, weigh about a third as much, and keep their voltage steady until almost empty, which is why they've become the favourite for portable radio.
Sizing the solar panel
Peak sun hours are the number of hours of full sunshine your panel effectively gets per day. In the UK that's around 1 in December and 4 to 5 in June. The panel size is your daily use divided by the sun hours, plus about 30% for charge controller, wiring and battery losses. Use an MPPT charge controller to get the most from the panel, and keep the cables short and thick: see the voltage drop calculator. For a single battery's run time, use the battery runtime calculator.
Questions
What happens when I connect batteries in series?
The voltages add and the capacity stays the same: two 12 V 100 Ah batteries in series make 24 V 100 Ah.
What size solar panel do I need for a 12 V radio?
For a few hours of listening and some transmitting each day, 100 to 200 W in summer, and much more for winter in the UK.
How deep can I discharge a battery?
About 50% for lead-acid and 80 to 90% for LiFePO4 for a long life.
How much current does a 100 W radio draw?
About 20 to 22 A on transmit at full power, and 1 to 2 A on receive.