Can I use this charger on a completely dead battery?

Yes. This charger is designed to revive fully discharged batteries. Attach the leads, plug in, and let it work—no special prep needed on your end.

What cables or connectors do I need to hook this up?

The charger ships with the unit itself. Verify the lead connectors match your battery terminals (standard automotive post sizes are common). You may need adapter clamps if your terminals are non-standard.

Is this safe to leave plugged in overnight?

Consult the manufacturer's instructions that ship with your charger—most modern base-model chargers are designed for extended charging, but confirmation from your unit's documentation is the safest call.