Probable cause is simply reasonable grounds to suspect that a person committed a crime. It is a very low standard, and a woman who reports that she was raped by a person named by her as the perpetrator will almost always give the police probable cause to arrest that person. The person you are referring to should meet with an attorney immediately and, if arrested, not say anything other than he is exercising his right to remain silent and wants an attorney.
Negligence is a civil concept that doesn't have applicability to criminal probation under most circumstances. If your probation officer tried to revoke your probation because you missed your meeting, her failure to give you reasonable notice could be a defense at a revocation hearing. However, as a criminal defendant you will not be awarded an early termination of your probation for your probation officer screwing up.
Hard to say without a lot more information ( which you should NOT provide here). The police also have the statements of any witnesses including yourself. Your boyfriend should retain counsel or apply for the PD immediately and not say anything else until his first face-to-face, privileged meeting with an attorney.
Police are required to issue Miranda warnings prior to conducting custodial interrogations. Your remedy would be suppression of any statements you made to police from being used as evidence against you, but probably not dismissal. You should meet with a criminal defense attorney to discuss further.
If there is evidence that would cause a reasonable person to suspect that you committed a crime, then probable cause exists for your arrest. A stranger's ID and credit card recovered from your car could result in charges of theft by receiving and identity theft, just to name a few. You should not discuss this with anyone else other than an experienced criminal defense attorney. I recommend contacting one immediately.
You won't have a case number until the court assigns one (which may take up to 2 or 3 weeks), and cannot get reports until they are made available through the district attorney's office in discovery, which typically cannot be requested until after your case has been assigned a case number. Neither of these issues, however, prevent you from consulting an attorney about your arrest.
The first thing you need to be aware of is your right to remain silent. DO NOT say anything about the incident that led to your arrest except to an attorney during a privileged, in-person meeting. Any admissions you make, online or elsewhere, can potentially be used as evidence against you if the prosecution gets a hold of it. You should definitely contact an attorney with experience practicing in Eagle County ASAP.
Your son should apply for a public defender immediately. I strongly urge you to not post anything about the facts of your son's case online or comment on his guilt or innocence, as such information could potentially be used against him if the wrong person saw it.