A settlement is fundamentally a contract where parties A and B promise to do certain things (one of them being "stop litigating"). A court order is an enforceable order to do something. A contract cannot be directly enforced (where force is used to make a person comply), it requires a court order for actual enforcement. The conditions of a contract might be ...
No, you are not obligated to provide the requested information.
You're out of trial court and into the court of appeals, where the civil discovery rules have basically no effect.
If the case gets kicked back to the trial court, you would likely be required to respond truthfully.
To cover your bases and look responsible, the most proper thing to do ...
There's nothing private about what you listed in #1; that's all publicly available information.
You can try to file an objection on the grounds of relevancy or proportionality, though we don't know the details of your case to say whether these would be appropriate or successful.
If this case has left small claims, you should be consulting with an attorney.