It's not clear what your question is. The only "reason" needed for a dissolution (divorce) in California is "irreconcilable differences", which means that one person doesn't want to be married any more.
The factors considered in custody are detailed in the California Family Code, starting at Section 3000. If you want advice as to how the code applies to the facts in your particular situation, you need to speak to an attorney. If you're going to try to handle the lawyering on your own custody case without assistance, you're going to probably have a very big problem on your hands.
A. You could tell the friend, politely, that he shouldn't call your number any more.
B. You could send a polite letter or e-mail to your ex requesting that he advise his friends that his number has changed.
C. You could ignore the calls from the friend, who would stop calling sooner or later.
Any of those would not likely result in a judge being unhappy with you.
D. you could send your ex an e-mail in which you refer to his "loser friends", and then describe doing so on a...
Not enough informatio0n to answer your question.
1. What are you trying to accomplish?
2. What hearings are now pending before the court?
3. What's the current custody arrangement?
When you have clear answers to these questions, you should discuss them, and the factual details of your situation, with an EXPERIENCED family law attorney. Child custody trial work is not a "do it yourself" kind of project.
I'll answer your question as much as I understand it. If your question is "Can someone who's alleged to be the father of a child refuse to take a paternity test, claiming that he has a constitutional right to refuse, and by doing so, avoid responsibility for his child?", the answer is a great big "NO." There's no 4th amendment right to refuse (it's not an unreasonable search and seizure) and if he refuses, the court can, if other evidence, including Mom's testimony is produced, decide that...