Accepting the facts exactly as you wrote them, your landlord was required to declare that you abandoned your property in accordance with the Arizona Residential Landlord and Tenant Act and then to store it for 10 days. If during those 10 days you made no reasonable efforts to remove the property then the landlord is free to dispose of it. Your landlord was required to use "reasonable care" in holding your property.
As for what is proper regarding damages, you would bear the burden of...
I believe you were properly served. As long as service was made directly on you, or at your home on an adult, service is good. Yes, a certificate of service should have been filed but it sounds like you are in Justice Court and the Justice Court judges are typically going to be very flexible about issues like that...I'm not surprised that the judge allowed it. Rather than wasting your time on arguing about procedure, it is probably best just to litigate the case on the merits.
To answer, go to the court which issued the summons. In Maricopa county, it is likely one of the justice courts or the superior court. Go to the self service center and ask for an answer form. There is an answer fee that you must pay at the time of filing your answer. In your answer, simply state that you are single and have never been married.
You probably are aware that Arizona is a community property state. A.R.S. 25-215(B) states: "The community property is liable for the premarital separate debts or other liabilities of a spouse, incurred after September 1, 1973 but only to the extent of the value of that spouse's contribution to the community property which would have been such spouse's separate property if single."
I'd recommend that you contact a commercial litigation lawyer who will give you a free consultation, take a look at the agreement with the carrier and help you determine whether you have a valid claim for a lawsuit and what your damages are. It is unclear to me from your question exactly how you have been damaged. You've got the product back. Were original shipping costs reimbursed since the carrier never made the delivery? These are issues you should discuss with whatever lawyer or lawyers...
It is unclear exactly what the agreement was. Perhaps a lease to own type of contract? In practical terms you probably don't need to do a foreclosure because the buyers are not coming back. Either way, you certainly need to determine if the buyers encumbered the property with any other liens while they occupied it.
I agree, you'll need to let a lawyer look at the entire contract. I've run into the provision before regarding the costs associated with the employees immigration proceedings. I do not believe such a provision is lawful. However, consulting a lawyer who specializes in immigration (which I do not) would be advisable.