Hi gavron.
To 1. : The order of the pins on the rectangle for the LTC6803-4 in the motherboard schematic is different from the order in the datasheet. On page 2 of the datasheet there is a pin mapping which shows the pin numbers and their functions like you where looking to the top of the chip (check page 38 too). The order in the schematic is different but the pin numbers map to the right functions.
To 2. : read → Battery is not charging - #25 by johkra
To 2/3. : The batteries are in series. Bat. 1-4 and Bat. 5-8 are bridged on the corresponding battery holder PCB / the two battery holder are bridged via the connectors J2 and J13 by a trace on the PCB (you can check it on the PCB exlorer: Interactive BOM for KiCAD
which is linked here: https://mntre.com/reform2-handbook/system.html. There is no common GND for all batteries. Bat. 1-8 and GND connections are to balance the batteries and measure the voltages and of course Bat 1. and GND are used to power the mainboard and to charge the batteries 