SolarNoobish

Just to answer one question. One cannot go against the laws of physics. Just like us after we worked hard and we rest we recover energy.  The same after you had a high load on the battery the voltage would recover as you have indicated in your tables. The same you will see that you get more Wh out of the same battery if you discharge at a lower rate. At a 25A load you will get more than 2 times the power than at 50A.
For the price you pay for your inverter to have an inverter, AC charger and MPPT you cannot expert it to be a Rolls Royce.
Normally one would use a lower setting for float than bulk. Then the inverter knows what you expect of it. Also I would use 44V for cut out to allow if the inverter over reads. Disclaimer: I don't have any Pylontec batteries but other lithiums.
Your observation is spot on that using voltage alone without looking at your actual load gives you a false indication of SOC. Perhaps using the volts at  no load will be more accurate. Also spot on why comms is much more accurate than voltage.
My suggestion is learn how best to use it for now. 35A for your battery might also be higher than the specs.

@Coulomb and @Piper
I did it ! Thanks to your advices, i finally connected it. Looks like it's working - at least the charging . 
She was near to empty, 21% ( voltage 48.2.) I am waiting her to get full and start discharging testing - i mean i'll cut-off the utility and see how it works and find the point of go-back -to-utility. Now i set it at 47V. It's too low, i mean i think this will go till empty battery. Maybe i'll go little bit higher, 47.5-48. I got a new toy !
Here it's winter, cloud and easy snow - so no PV input, only 2-300w. Perfect day for testing it.
I set the limits in area you advised me.
I set the charger current low than 25A - my inverter has 20A and next 30A. So - i go for the lowest, just for safety - cannot be bad, willl take more time to charge and limits power , but i am testing, this is  first day.
A big-big-big, a giant THANK YOU for all your time spent with me and for valuable info you gave me.
You can't imagine how helpful you were. I don't know how to thank you...