Get an immigration lawyer right away to help her. There is a very real chance that she will be deported/removed unless she has the help of an immigration attorney.
Yes. Unfortunately, he can be given all the time he could have been given on his first case (the one he is on probation for), although he will probably get credit for the time he did on probation before going on the run. That credit will be counted towards time against any time he might be given by the court. He can also get time on his new case. It really sounds like this person has a serious drug problem. It might be worth trying (again) to get the court to force him or her to go...
You may be arrested if enough evidence is found against you. New Mexico will be able to extradite you from another state in the US.
Yes. Expired tags is enough for a stop.
Even if the charge for which a person is arrested is dismissed, he can still be charged with resisting the arrest in the dismissed charge. The resisting charge is not related to the battery charge. It is only related to how the person behaved while being arrested.
The type of charges he has should not make a difference. Once the judge orders a person released, the jail must release the person. It may be that the district attorney is taking his or her time filing the order for the court to find, but that is no excuse. A motion should be filed (by the defense attorney) to release your husband right away.