With so many convolutions and issues raised by your post, it seems clear to me that you should work with an attorney experienced in divorce to address these issues. There are some highly qualified attorneys in Sedona that may be able to provide you the information and knowledge you seek.
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You may have a statute of limitations because that begins to run when you knew or should have known that you might have a cause of action. You don't have to know exactly what went wrong, only that something went wrong, such as never being served or accepting service. Keeping this in mind, I also encourage you to discuss your case with an experienced family law attorney to see if you have any options.
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You do not need to have signed an acceptance of service for a default to be entered. To get an entry of default the person just has to be served. Service can be effectuated many ways including publication. You must first determine the method of service. If service was completed by some valid means you are stuck if the default was entered. You can seek modification of certain orders but not all. If service was never effectuated and the default was entered improperly you may be able to set aside the judgment; however, the court normally only does the judgment is challenged in a reasonable time ie normally 6 months. 7 years is too long. You would need to speak with a family law attorney to help you with this but you are most likely only going to be able to modify not set aside. Also if child support was incorrect, it does not matter, the court will not retroactively modify the support order. You will owe that money. You may be able to modify current support. If you want to look at the rules go to this link: http://www.supreme.state.az.us/rules/ramd_pdf/R-05-0008.pdf and look at Rule 44 and 85. Good luck.
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