1) yes. Portable battery charger with 5+ amps rating should get you through. Direct on the battery. No need to disconnect anything.
2) OK to change models however the PD9145 is an excellent converter. Get the wizard controller with the replacement or a PD9245 with the controller built in.
3) Check the battery is in good shape. Also post if any battery or other service has been recently done that could have caused the converter issue. Also verify there is nothing blocking airflow around the converter.
https://www.bestconverter.com/PD-9245C-45-Amp-RV-ConverterCharger