Yes, but chances are you wouldn't even know you're pregnant at three weeks as this would be a week before your period is due.
If you mean a week after a missed period this is 5 weeks pregnant. any...
Yes, in the US the limit is around 20-24 weeks. The average price for a medical abortion is $400. All clinics and hospitals have individual price settings.
You can only have one for health reasons after week 20 and then I imagine your insurance would pay for that since your life would be at stake. It's thousands of dollars though.