Is it possible to monitor the battery SOC for a 48 V battery with an Arduino? If not, which device would you suggest? If the battery is at 85% SoC, it should be re-charged, triggered by a relay.
If charge voltage and current suffices, then pretty much any microcontroller with access to sufficiently accurate ADCs will suffice.
Use resistive dividers to reduce voltage to levels compatible with the ADC, and low side shunt ideally with differential ADC (or dedicated current monitor) for dis/charge monitoring.
For completeness, add a remote temperature sensor.
LiPo/Liion is more complex, as voltage monitoring may not be sufficient for long term stability, and you may need coloumb counting.
Yes, it is. You would take a voltage divider to get the current voltage down to a range that the arduino's ADC can observe ("Arduino" doesn't actually mean any specific hardware, but all different implementations of the Arduino platform have some sort of ADC).
Depending on the battery chemistry and speed of charging, you'll also want to track the current that flows into the battery. How you do that depends on the currents and what you use to control these currents – it might be as simple as a shunt resistor and two ADC channels, or as complex as getting current estimates from an integrated switch-mode controller.
Generally, Arduino is really not the type of platform you'd want for that. There's ready-made charger control ICs for most battery types.