Hello Guilherme,
Hope you're doing well.
First of all, yes it is possible to debug your code in Production environment.
For that, you should go into Service Center -> Administration -> Environment Configuration.
You will see a check box with the option Debug Mode that you will need to tick.

However, let me tell you that this is not recommended at all. It is not the purpose of this environment to do debugging for the most obvious reasons (people can be accessing to your applications at the moment). Also, Production environment should always be a highly stable environment because end-users are accessing to it.
With that said, and responding to your other questions, there is no option in Service Center to switch the order between two environments. The Service Center is a tool that applies only to a single environment.
If you want to manage the environments across your entire infrastructure, that is only possible using LifeTime tool.
Just go to LifeTime -> Infrastructure and you can manage your environments according to your needs.
However I would like to suggest a different approach for your scenario.
Usually what you should do is to migrate the code that you have in Production to another environment (Pre-Production) and debug the code in there. Once you find the bug, you fix the bug (hotfix) and you can migrate the code back to Production. After that, you should replicate these changes back to Development and Quality environments.
If you don't have a Pre-Production environment, you should use Quality environment for this purpose.
Hope that this helps you!
Kind regards,
Rui Barradas