Extension cords are fine. Inverters need pure sine.

Yes, you can use an extension cord with a power tool battery charger — but the inverter question is a separate thing.

For the extension cord: keep it short and thick. An 18-gauge 100-foot cord will drop voltage enough to slow charging or heat things up. 14-gauge or 12-gauge for runs over 50 feet. That’s it. No special magic.

For the inverter: