Thank you Mav for the reply!
Concerning your first question:
When I first installed the pack the initial battery SoC was ~70% as indicated by the PC Software (which connects to the BMS) and the same SoC was reported on the inverter after successful communication of the battery pack with the inverter.
Then, I let the battery charge from the PV arrays (this is DIY off-grid system, there is no AC input) and after a few hours (of very low sunshine, it was November) I saw a sudden jump from 75% to 100%.
Nevertheless, the next day, I left the battery pack to remain at 100% in order to balance. However, I don't know if this ever happened, since the BMS-inverter communication was in any case so bad, I have no clue if any balancing took place. At least I tried

A day later (after spending 24hrs at 100%, a small discharge during the night and recharge of this lost percentage in the morning), I decided to test discharging the battery. I plugged in my mobile phone and everything worked like a charm.
However, when a higher load was plugged in (2.6kW) the SoC immediately dropped to 5% and the inverter stopped the AC output supply.
Letting the battery charge without a load returned the SoC to 100% after 30 minutes

Now coming to your second question:
Last Sunday I went back to my pack, opened up the cover and started checking the wiring and did some continuity tests on the BMS balance leads. Everything seems OK, but I probably need to test once more after disconnecting everything and removing the busbars. I also measured the battery cells individually and they were all around 3.23 V with minor differences between them (I guess that's good news).
As you mentioned, I can verify your remark about the discharge MOS, where I get an error in the PC software (see attached Figure).
Probably the BMS settings are totally off, but no matter how many times I have asked BASEN to provide me with a list of the recommended settings for the LPF batteries they tell me to fully charge and discharge

. I guess even if I go back to them and say that the whole battery pack is on fire, they will probably recommend the same action.
Finally, concerning the comms, yes, it's been the last 3 months that I have been using the pack without any comms with the inverter (they never worked together) and used the inverter 'custom' battery management mode, where I used a float value of 54.7V, A charge voltage of 55.2V and a cut-off voltage of 47V. Things worked (almost) fine, until the last 2 weeks, when I realized I cannot charge using a current higher than 5A and cannot charge beyond a voltage of 53V....
This is my first DIY battery pack installation and I thought it would be easier, but unfortunately I underestimated all the factors and things that can go wrong, along with probably the worst customer service I have ever experienced...
Again, thank you for the reply, much appreciated!!!
Here is the PC software status screenshot and a picture from my pack:
View attachment 279154
View attachment 279155