The DMV is a governmental agency with employees that are well known for making mistakes. And the tough part is getting them to correct such errors. It sounds like a mistake was made here. So take all your paperwork to the DMV and see if they will straighten it out. If not, you can file a writ of mandumus in court that will compel the DMV to correct its error.
You should definately contact an attorney. If money is tight, and you don't want to forfeit the amount that the bail bondsman charges, we can likely get him released without bail, or get bail drasstically reduced at the arraignment. The DA might be able to offer a very good deal becasue the facts against him are very weak.
Yes, your son could still get in trouble. But it comes down to whether the DA believes her, and not your son. Your son should not discuss this issue with anyone accept an attorney. If he is contacted by anyone, he should direct them to contact his attorney.
Suing the government is a painstaking and expensive process. Government employees are given great deference in their duties, meaning that they are allowed to make mistakes without being sued. So you would need to prove that their actions were beyond that level of deference. Here, there was information linking you to the suspect, and that may be excuseable.