The converter is essentially a regulator designed to ensure that batteries are not overcharged. Output should be around 14 volts to charge typical lead acid battery without damaging it. For a battery, I would probably choose a lead acid battery and just leave the current settings alone. Not advice and I recommend following recs by others on battery choice and settings.

Yes, the night-time operation would work like you thought.

It isn't what we don't know that gives us trouble, it's what we know that ain't so - Will Rogers