Well in general; no it is not normal for battery to be low after a drive, with a working alternator battery should be pretty well charged after about 20 minutes of freeway type driving.
I don't know your battery but the math works like this, 600 CCA battery will take 15hrs to fully charge at the ~ 4amp charge rate your charger has. That's why yours took till 8am.
I'd say you have a bad alternator. A chain auto parts store will usually check for free. Hope this helps.
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