novice rebuild help needed - make help & troubleshooting throttle issue

My son was given an electric moped and as a project to help him develop the skills to go about a task in a planned orderly way (he's 12 years old) we are rebuilding it to get it going again (its been lying unused outside for some time before he was given it).

He will only ever use it on private ground until he is old enough to use it legally and only under my supervision but I suspect it may be a while before we are finished!

Im not the most mechanically minded person ( desk job) but since its basically a bike with an electric motor I thought its something we can do together.

There are a few issues with it at the moment
* the key is broken in the battery lock ( my brother is a locksmith and can make me a new set of keys)
* the batteries were dead when we got it
* some dodgy bodywork damage we can repair and respray
* broken front brake lever
* do not have a bespoke charger for it
* runs at full throttle when fired up ( but see below how I did this without the key)

But other than this we have stripped it down to the frame to clean it up and repaint it and it looks pretty solid.

I charged the batteries manually using a good charger for sealed batteries charging each individually disconnected from the rest of the moped. I then sisconnected the ignition barrel wires and connected the two wires leading to the ignition after connecting the batteries and hey presto! The rear wheel sparks into life at an indicated 30 kmph and seems to have plenty of torque. So having run it for a while without any immediate loss of charge or speed Im happy that the batteries are good.

The throttle doesnt work though - turning it makes no difference to the speed of the wheel - and seems stuck open. I disconnected the throttle wiring and tried again hoping that it would not move and it was therefore the throttle grip that was the problem but it still fires up at full speed so I think I need a new speed controller.

The problem is I know it is chinese (characters on the badge and controller are a give away) but I have no idea what make it is and I cant find anything on the internet under different combinations of possible names (fancy font on the badge that could be interpretated several ways!)

The batteries are 10AH and 12v connected in series making it a 36V machine.

Ive attached a pic of the front logo for anyone who recognises or can tell me how to find parts:

Also a pic of the speed controller

Could anyone suggest
what else I can do to try and rectify the throttle issue
what spec I need to consider for a new controller if that is the problem
where I can get replacement charger/brake lever

My son is very keen to get it back up and running and wants to reair and respray the body work - I think its a great wee project for him but it would be a shame if we have to spend a lot of money on it.

I reckon that we can stretch to a new controller, charger and brake lever and it would be great for him to see this one through having never shown any interest in hands on work before ( X box /instant gratification generation!)

Any help you guys could give a novice like me would be greatly appreciated by both me and my boy.