My unit is at home right now so can’t double check the specs on the charger but typical chargers like this are in the range of 60-100 Watts and will not be power factor corrected so you will need a 300 Watt inverter minimum due to the high current pulses. I would recommend a pure sine wave inverter, just in case and for longevity.
The charger has a universal input at 120 or 240 VAC, refer to the specs. I would not recommend going direct DC for charging, Lithium batteries can be fickle and not using the supplied charger is a recipe for disaster.
Using a 100 Watt solar panel charging a battery (your inverter attached to the battery) assuming optimal solar conditions it should be more than enough to charge the 95 Wh capacity battery (refer to the specs).