Moped has electric problems, plus the electric starter won't work?

This isn't about cars, but it's about my moped. I have a 2007 49CC Black Cat Genuine Moped, but I have a few problems. First is with the electric start, it does not work. I think it's the battery but not sure, when I hook a Battery charger up to the moped and set it at 200 amps the electric starter works fine and starts it immediely. I've tried charging it over night, but the moment I take the clips off the electric start does not work. It does not even try to turn the motor, no sounds occur when pressing the button. Is it the battery? The battery is new also I believe, cause I bought it last year to see if it would fix the problem but I don't think it did. The second problem is with the wiring, the blinkers in the front aren't working right. It will either light up and not blink at all, blink every 10 seconds, or not even turn on at all. When doing this there is a errrr ehhhh kind of sound coming from the front of the moped, also the oil light is glowing even though the tank is full. What do I need to do to fix this?