Hello,
In what order will the groups be executed? Really the order I'm choosing with the "up/down" buttons?
Yes, that is correct.
What if I place more than on group with "If the operations succeeds"?
You can have as many action sets in a Business Rule, Custom Command or Scheduled Task as you need. For Business Rules triggering after an operation (e.g. After creating a user) it is recommended to keep the If operation succeeded condition to avoid triggering the rule if the operation fails or gets suspended.
What if I change some field in the first group and use that in the secons group? Variables are replaced on triggering completey for the rule, aren't they?
If you update a specific property value in one action set and then try to use it in another set, the second set will get the old value of the property. To get the new value in the second action set, you can use PowerShell scripts.