Lol, yes, quick cure is common.
Use it for probably 3 days or until the fish are clear. I recommend adding salt, and boosting the temperature as well.
It's common that quick cure will dye your silicon lining in the tank, but over time slowly fades away.
You can keep the carbon out of your filter for however long, as long as the tank is fully cycled. If it's fully cycled there should be enough bacteria on the gravel and decorations in the tank to keep things nice. You might experience a very small amonia spike, not enough to harm the fish though.