What happens when you go to court to see if a judge will open a case?

I assume that what you are trying to ask is if the judge will agree to review and revert, revoke, or modify the original decision. Maybe whoever used the phrase "opening the case" just misspoke the wrong terminology by mistake (we are only humans, we make mistakes sometimes.)

In any case, this is basically what will happen: you go there, you sit, whoever petitioned the court hearing will have a chance to present his/her arguments (most likely an attorney will do that for the petitioner), the other party will present their arguments opposing the petition (assuming they are opposed.)

They family court judge might ask some questions, and might want to hear or read the recommendation from Child Protective Services's case worker.

Depending on how complex is the case, the judge might made a ruling the same day or set a new hearing date so that he/she can have more time to review both parties' arguments and evidence before reaching a decision.

Generally speaking, cases are "opened" when somebody files them. Judges don't decide to "open" cases at court. They may decide not to reopen a case based on somebody's motion to do so.

Despite your update, there's not enough information here to know what will occur and why. It sounds like someone is asking to terminate a guardianship. But saying there's a "guardian" while simultaneously saying "the parent never lost custody" doesn't make much sense.

No, issues usually are not solved the same day unless everyone agrees. If there's any dispute, and there needs to be a hearing, that's usually scheduled for another day.

That might depend on some little details like what the case is, what evidence there is, etc.