Apart from the design difference - the biggest difference is AirPods are wireless while EarPods are not wireless. The AirPods comes with lot more openings compared to EarPods.
Yes, you can connect Airpods with iPhone 6.
When you open the case, the light shows the charge status of the AirPods when they are inside the charging case. When you remove them, it shows the battery level of the charging case. Green light means they are fully charged and you do not need to charge immediately, while orange light means you need to charge them now.
Yes, you can control the volume from the phone using the phone's volume buttons just like we do in case of any other headphones.
Look past their offbeat design and you'll find that Apple AirPods' compact size and high convenience factor are a winning combination.