C) John, if searched in the CB database, will be shown in the list of the users.

When searching where? On frontend? If on a frontend userlist it maybe better to just exclude users who have expired certifications entirely, which you can do by adding an Advanced filter to your userlist. This can be done as follows.


Replace FIELD_NAME with the name of your date field then add this to your userlist under Filters after selecting Advanced. This will add 3 years to the date they supplied and check if it's greater than the current date. If it is they aren't expired and will output in your list. If it's not then they won't show in the list at all.

CB Auto Actions performs actions on events. You don't have an event for it to act on. So your only options are to run your auto actions on every user on the site using Internal Users and a CRON task or acting on something like onAfterLogin to perform the action anytime a user logs in. Neither of these are perfect solutions for what you're trying to do since CB Auto Actions is not a scheduler. It just performs actions on specified events automatically.

A ) when "today" is the day of the expiry of the certificate,
CB AA should unpublish the user from the userlist in the frontend.

You don't need an auto action for that. My above Advanced Filter added to a Userlist will do that automatically for you.

B ) when "today" is the day of the expiry of the certificate,
CB AA should send an e-mail (if doable) to the user, telling him "Hey your certificate is expired!"

Only way to do that is to create an auto action with Triggers set to Internal Users. This will cause the auto action to execute against every user on your site when you run the Internal Users URL in CB Auto Actions > Parameters. Typically you schedule a CRON task to perform a wget against that URL regularly. In your Conditions is where you would perform your date check, which would be as follows.

Global
Triggers: Internal Users
Type: Email
User: Automatic
Access: Everybody
Conditions
Field: Custom > Value
Custom Value: [cb:parse function="time" time="+3 YEARS"][FIELD_NAME][/cb:parse]
Format Functions: SELECTED
Operator: Less Than or Equal To
Value: [cb:parse function="time"][cb:date format="Y-m-d" /][/cb:parse]
Format Functions: SELECTED

Replace FIELD_NAME with the name of your date field. This condition would allow the auto action to execute if their date field with 3 years added to it is older than the current date. Please be sure to read parameter descriptions carefully. CB Auto Actions is an advanced tool and it is not recommend for those completely new to CB; you can review System Actions in CB Auto Actions > System Actions for examples and inspiration as well.

Ah, ok since they've supplied the expiration date you don't need to do any additions to the date then. So for your userlist you'd just have the below advanced filter.


For your auto action condition you'd have the below.

Field: Custom > Value
Custom Value: [cb:parse function="time"][FIELD_NAME][/cb:parse]
Format Functions: SELECTED
Operator: Greater Than or Equal To
Value: [cb:parse function="time"][cb:date format="Y-m-d" /][/cb:parse]
Format Functions: SELECTED