You have a lot of questions. Probably too many to answer on a forum like this.
1) You can simply call the court clerks at the courthouse and provide your name and date of birth and the year that you got the divorce and they will gladly give you the case number over the phone. There is no requirement that you physically drive down to the courthouse to visit with the court clerks in person.
2) If he quit his job to pursue his dream, it depends on whether such was "a good faith" career decision that will ultimately lead to him earning either the same salary or a higher salary. You simply can't just quit from being a doctor or a pilot and work at Starbucks. So, unless he can show that it is a good faith career choice designed to get more salary in the future, he will likely be unsuccessful in his attempts and be deemed to be "voluntarily underemployed."
3) If he is not paying his child support, you do HAVE to file a Motion for Remedial, Indirect Contempt to have the judge order him to pay the child support or look at 6 months of jail. As a former judge presiding over child support cases, I can guarantee you that the prospect of 6 months jail serves as a great incentive in getting people to pay child support.
4) You REALLY need an attorney on your case. Whether a free one through the DU or CU Law Clinics, Metro Volunteer Lawyers Association, or Colorado Legal Services or through one of us attorneys who work with low pay/slow pay clients.
The information provided in this answer does not create an attorney-client relationship and is not considered to be legal advice. Mr. Leroi answers questions on Avvo because he strongly believes in public service from his years as a judge, magistrate, and prosecutor. If you need to ask any follow up questions because my answer did not fully address your question, feel free to call Chris or post an additional question. Thank you.
Mr. Leroi nailed this answer -- you ought to consider using him to deal with this situation.
In no way am I offering you legal advice, and in no way has my comment created an attorney-client relationship. You are not to rely upon my note above in any way, but insted need to sit down with counsel and share all relevant facts before receiving fully-informed legal advice. If you want to be completely sure of your rights, you must sit down with an experienced criminal defense attorney to be fully aware of your rights.