Building a solar phone charger, how does a solar panel charge batteries and what voltage should the panel and the batteries be?
What you need to do is to buy both step up and step down converters.  During the day, you use a step down converter to charge battery from your 5V solar panel. When you need to charge your phone, you use the step up converter to convert 3.7V up to 5V.  

There are couple issues you need to watch out.  First, you need to find proper step down converter.  Most step down converters are regulator (fixed output).  They are OK, but not ideal because the voltage of battery changes after ages and you have no control of how much power goes in battery.  It may cause damage of the battery and inefficient charge. 
Then, when you buy your step up converter, making sure they are capable of 2 amp. You don't need to measure the current since you have a fixed load (basic physics 101, fix voltage and fixed load gives you fixed current)
Also, using AA battery not gonna fly because they output power of them are too low and the capacity of them is very small. You need something having output power 10 to 15W (3.7V with 3A at least).  

There are also other aspects I didn't cover. You need to do a lot more research.