How long to ferment for?

I've done a fair bit of beer brewing and I have started my first cider brew a few days ago from a Brigalow kit. How long should I leave it to ferment? I'm not going to do secondary fermentation. The OG was 1.038, so what can I expect the FG to be?

I've never heard of that kit, so I'd just have to guess but I'd say it should finish dry maybe .990-.996 or so.

depending on the yeast anywhere from 1.002 to 0.990. wine yeasts will take it much drier, ale yeasts keep it with a little more sugar, most of mine end at 1.000

Should I leave it to ferment for 3 weeks?

You've done brewing before so you're already set. Just take readings for a few days after your airlock slows down a lot or stops. With cider, keeping it in the fermenter longer isn't likely to hurt it. If you're using pressed apples where the juice isn't properly strained and you have a thick must, leaving the cider on it's lees for too long without racking it off can cause the cider to absorb some off-flavors and it can get a yeasty taste. This takes months though. Three weeks should be fine, especially if you're using a kit.