.... your connection is not private i proceed to the website ...
What are the steps to take after adding an invalid certificat authority?
You probably did not add a new certificate authority. If you simply clicked to make an exception in order to proceed you've only added an exception for this specific certificate used on this specific site. This is different from adding a new certificate authority (CA) which would be able to issue certificates for lots of sites. Steps to adding a new CA are more complex then just agreeing to add an exception.
The steps to remove an exception you have added to a browser depend on the browser. Google will help when you ask the right question.
in the future, how can I proceed to the payment of my bills safely and without using a VPN?
If you get a security warning only for a single specific web site then chances are high that this is caused by a bad certificate on the site itself. Contact the site owners in this case so that they fix it.
But if you get such a warning for most sites then either the time on your computer is way off and thus most certificates are considered not yet valid or already expired. Or there is some SSL interception going on (i.e. man in the middle). This might be legal if you are inside a company and you should contact your local administrator on how to proceed. If you are in some public network then it might be caused by a hacker playing with the customers and you should not proceed. If this happens inside your own network something is very wrong there which you should fix before continuing with sensitive transactions.