Yes, the gearbox will need to be taken out of the car. Since this is a front wheel driven car, it's a bit more complicated than taking out the gearbox of a rear wheel driven car. Plus, you might have to get a wheel alignment done after the repair, depending on which suspension components need to be taken out to access the gearbox.
As for labour charges, I guess it depends on the place you take it to. I've been away from the country for a couple of years now, so I don't think I'm the best person to give you an indication of labour charges. Hope someone else can answer your question.