The battery isn't rechargeable, it's a lithium thionyl chloride, and is only 3.6V when new. The ones using 18650's I'm 'playing' with don't have charging capability, and you simply unplug the battery to recharge it, if needed.
There isn't a driver, the dual FET is used as a power switch - by removing the power to the converter when not in use it reduces the power consumption of the converter to zero. The converter chip has it's own on/off switch, but consumption is still too high when turned off - remember I'm aiming for 5+ years battery life.
No mains voltage, so no need to convert it down - in fact where the devices are installed it's VERY unlikely there will be any mains anywhere near.