What protection circuits do laptop batteries come with?
That method will work fine. In fact many hobbyists similarly repurpose laptop batteries as universal power supplies, e.g. see here. Beware that some laptop batteries also require that another pin be grounded to enable output, e.g. the "System Present" pin on Dell batteries - see the linked page.

There is no need to worry about overdischarge since all modern laptop batteries incorporate a battery management system that includes overdischarge protection. It will disable output when any cell reaches too low voltage (typically between 2.8V - 3.2V).

Laptop batteries don't typically include any voltage regulation, so the output at the terminals will indeed decrease as the cells drain, typically from around 12.6V to 9V for a pack with 3 cells in series, or from 16.8V to 12V for a pack with 4 cells in series. More recent packs may use cells that charge to 4.35V so then the fully charged packs will be 13.05V and 17.4V respectively.