If I am not mistaken, a brand new battery is not fully charged when delivered due to the shelf life of the battery. basically habang nasa shelf siya (hindi pa nabebenta) dahan dahan nauubos ang charge.
Yup, but AFAIK, the moment the car starts, the alternator begins charging the new battery. So, within 30 minutes, dapat fully charged na yung battery.

Am also inclined to think na baka maluwag nga yung terminals. Pero according to the TS, tuwing naka-neutral lang daw namamatay yung makina eh. Hmmmm...