1. It depends on the size and length of the wires going to the batteries. For example, 30 feet of 12g wire can't carry nearly as much amperage as 2 feet of 4g wire. You need to see what gauge wire was used and estimate its length. Then get back to us. Also, there is a breaker between the converter/charger and the battery. You need to know what size it is.
2. The solar charge is separate from the converter charge. The solar charge controller is connected directly to the battery and doesn't even know the converter/charger is attached. There will be no conflict.