Sorry for late reply, cheap battery like AC delco have a life of 1 - 1 1/2 year only. Go with good slightly expensive battery like Exide, Amaron, Trane etc that will last atleast 3+ years.
If want best battery go for Optima as they come with 5 year warranty and will last 5-7 years easy but it costs 4 times than the normal battery cost as its a deep cycle battery.
What you study is one theory, that may be specific to coupe.
But considering checking or changing the gear oil and gear filter, when you feel gears are jerky. Usually gear change is done at 40k -50k, if you dont have previous record its better worth the change than building the whole gear later.
Under normal conditions if the SRS warning light is not on. I suggest that you contact Hyundai direct and talk to customer relations. and they can advise you how to remove it.