Yes, charge the light for the full time stated in the instructions and pay no attention to the charge indicator light on this first charge.
Yes, this is dependent on the light but we do for some lights, contact our customer service line at 877-269-8490, Option 1 for help.
Yes, with the sealed lead acid battery you want to maintain a steady charge. Make sure you are charging your battery fully every 90 days whether you are using the light or not to hopefully avoid battery going completely bad.
Some Cyclops lights will not work while plugged into the AC charger, but will work when plugged into the DC charger.