Can I use an extension cord with a power tool battery charger, and what about inverters?

Yes, you can use an extension cord with a power tool battery charger — keep it short and thick. An 18-gauge 100-foot cord will drop voltage enough to slow charging or heat things up. Use 14-gauge or 12-gauge for runs over 50 feet. For inverters, you need a pure sine wave inverter — that’s a separate requirement.