Your salary will be "grossed up" to offset US taxes. Raises are small and once a year. If you don't have children, it will probably be a three-bedroom apartment. They will not lower your salary because of your choice. The decision and contract will be offered later, you have as much time as you need to decide. Yeah, since they are paying for two business class airfares and a 5-star hotel, they are very interested in you.
Mandi