The type 1 and type 2 is what you will use for normal operation to stop a charger or a load. In case of LiFePO4 default will be 3.55V for 6 seconds for type 1 and then charge source will be stopped as battery is fully charged similarly for type 2 the default limit is 2.8V (below that the loads will be disconnected as battery is empty).
type 3 and 4 are based on SOC only so are good just as alarms mostly as SOC may be calculated incorrectly depending on how well you make the settings and how accurate is your current shunt. But they will also react as type 1 and 2 based on voltage so say you set a Load as type 4 and set the SOC to 30% then normally when battery is below 30% the Load will be disconnected but if for some reason the SOC is not correctly calculated and say SOC is 50% but one of the cells is below 2.8V then the Load will still be stopped as the cell low voltage will bypass the SOC setting.
Type 5 is the one that will react to under or voltage lock settings as those are secondary limits set at 2.5V and 3.75V default and cells should never get there unless something is faulty or installed incorrectly. So type 5 is usually used as a second level protection normally tripping a breaker and yes you will need to have separate breakers or breaker contacts for charge sources and Load's but they will be both tripped at the same time just kept separate trough separate contacts.
If this happens it will be abnormal so it will require manual intervention to restart the system and the cause should be investigated as it will not be normal operation.
Type 1 and type 2 will also react to voltage lock limits so say you have an inverter charger but you incorrectly only installed a type 2 of the inverter as remote ON/OFF and you connect the grid charger then battery will charge to 3.55V but since there is no type 1 connected to stop the AC charger (inverter run in reverse) then battery will continue to charge until 3.75V when the type 2 will also become open circuit and stop the inverter that hopefully will also stop the charging.
So all you need is normally just type 1 and type 2 as if those are installed correctly and tested (by setting them to type 0 and see if all charge sources and Loads are turned OFF). The type 5 can be used to trip a breaker (maybe one with two separate contacts or two separate trip breakers) but it is likely that will never be used as it is super unlikely for a remote ON/OFF on a device to not work. When is last time you turned OFF a device using the power ON/OFF button and it continued to stay ON?
EXT IOx are opto isolated switches based on Toshiba TLP172GM with closed circuit for ON and open circuit for OFF so if one of the two EXt IOx wires is broken the device controlled by that will default to safe OFF position.