There is no set amount of time for fermentation let gravity be your guide. after a couple weeks take a gravity reading, wait three days and take another. If it has changed, wait another three days. if it has not changed and it's more or less at the gravity you expected it to finish it is finished.
if you do not want to force carb in the keg you prime with sugar just like in a bottle but less. Find an online carb calculator or use a brewing software is easiest but as a ROT, depending on style around 3-4 oz of table sugar should do the trick, you will still want to hit the keg with a little co2 to make sure the lid seats well.
to force carb I set it at service preasure and rock the keg back and forth until no more gas goes into the keg (you can hear it hissing) or until I get tired. Then leave it for a couple days.