I believe the above is pretty normal as I've seen it like that everywhere I've been. At least, it's normal when you have a root domain etc, as I do, and as I would say with some degree of certainty that you do too!
So your 'child' or 'resource' domain is domain.state.country, and your root domain is state.country (or with state and country as separate domains). At least that would be my guess. Though why the initial 'primary' suffix is duplicated I don't know. I could take a complete guess that when you have the 'Append primary AND connection specific DNS Suffix' option checked, and the primary + connection specific suffixes are in fact the same, that is might add both to the search list?
And no, we have absolutely no DNS issues of any kind whatsoever!!