I have replaced your code in frontend and backend but I have not resolved the problem

Kindly please elaborate your problem and also place pic for the error condition. I can't understand where the actual problem you are facing

1 step: I add a new field in "Custom fields" with this options:
Field Type: Check Box; Required?: NO; Read Only?: NO; Publish: YES;

2 step: I go in section Vehicles->Vehicles
before section "Vehicle options (check any that apply)" there is the new field added

The problems are:
1) the new field is always checked and it's impossible to remove the check (backend)
2) in frontend the new field is always visible and appear with the reference "true" or "false"

Open a support ticket