The battery is 9ah and the solar panel is 20w
Buy the proper charger or get a degree. Don't screw with making a charger for a lead acid battery of you don't know what you are doing. You could get hurt. You need a hell of a lot more than just a regulator.
Yes, certainly. So long as the solar panel's voltage exceeds the voltage of the battery (which is probably going, certainly if it can be a discharged battery, which is lower than 2 volts), then it will recharge the battery. Additionally, a 2 V solar panel can produce bigger than 2 volts. Nevertheless, the rate of charging is more likely to be depdendent on the availabilty of daylight. And of course, the better the capcity of the battery, the longer it takes to cost.
You need a switch mode voltage converter, made to input 2 to 20 volts, and output around 7 volts. Some cell phone chargers can do that, or be modified for that voltage. Option B is to get another battery and use the system at 2V, and regulate that to 6 or 5 volts for charging (you can directly use your car charger), with switch mode regulators. I would find that system to be more flexible. Getting an 8Ah would leave extra capacity. BTW, for a 9AH battery, 20W is kid of big. I have a 36Ah battery and a 20W panel, and that is good for it.
despite the statements to the contrary, using a solar panel to charge a battery is not rocket science. first lets look at you panel. panels normally have a spec for open circuit voltage (probably 20 volts for yours) operating power (4.4 volts at .4 amps is usual for 20 watt panel) and short circuit current (probably 2 amps in your case). if this panel is connected to a 2 volt battery, it will develop 20 watts of charge current in full sun. if this panel is connected to a 6 volt battery, it will work closer to the short circuit current or about .8 amps. doing the math this is a 7.2v x ,8= 3 watt charger for 6 volt batteries. while it is less efficient than when working at 2 volts, it will still work pretty good and no regulator is needed if you remember to disconnect the panel after 5 hours of full sun. if you want to walk away and have it run automatically, then you will need to find a 6 volt charge controller.
