Yes, you have 30 days per Rule 4.2(m), Ariz.R.Civ.Proc., to respond to a complaint when served outside the State of Arizona.
Yes, if the damages are not stating in the Complaint, and sometimes even when they are, the Court will hold a hearing to determine damages. It is not a "default hearing," because by that time default will have already been established. It is simply a "damages hearing" where the plaintiff's put on basic damages evidence and request a judgment for the specific amount. Unless it is contested, the Court will generally accept reasonable requests at these hearings.
While I am not licensed in Arizona, my colleague has nailed the Arizona law as it relates to the timing allowed an out of state defendant and default hearings. The process is similar across the counrty.
I wanted to add a comment -- it a default hearing indeed takes place, if the out of state defendant comes in relatively soon thereafter to contest to findings, there is a chance the court would re-open the case and vacate the default judgment.
Best of luck.
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.
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