As a former Hyundai Sonata owner, I can confirm that the only things they would willingly cover under warranty were recalls (5+ of those) and if the check engine light came on (twice). Otherwise, they would claim other issues were simply "normal" and not covered under warranty.
At 30,000 miles, I asked them to investigate why the drive belt would squeal while driving in heavy rain and the battery warning light would come on at the same time. They said "we will look into it, but understand if we find anything it is not covered under warranty since it involves the drive belt which is a wear item." I said to them "the car only has 30,000 miles on it and all service has been done here by you." They responded "Sorry, simply not covered by warranty if there is a problem." They did their check, claimed the belt was fine as well as the belt tensioner and pullies. They finally said it was "normal" and not to worry about it. Thanks, that's great. After that I never bothered to ask them to investigate why the instrument cluster would randomly go dark and the car would lose all power for a few seconds. I am guessing that would have been "normal" as well since it would never throw a code when that happened.
All oil changes were done by the dealer. They suggested a 6,000 mile interval. I would go in every 5,000-6,000 miles. By the time I traded the car with 72,000 miles on it, it was using 1qt of oil every 800 miles. I was adding 6-7qts of oil between oil changes (not sure why I even bothered getting the oil changed at that point since it was constantly getting topped off.) No leaks. It was simply eating oil. A few months after trading it, the engine recall was announced.
Monkeyman is fine using the 5W-20 synthetic in 5,000 mile intervals. Definitely stay with the OEM filter. Hyundais can be kind of finicky with aftermarket filters. They will work, for sure, but OEM is best for Hyundai. Keep all of your oil change receipts and make sure everything is documented. Don't get overly concerned with the normal vs. severe service. Hyundai makes it sound like everyone is severe service. As long as you use the OEM filter and synthetic oil, splitting the difference at 5,000 miles will be fine.