1, you need to fill out a form on the FAA website here:
Airmen Certification: Verify the Authenticity of a Foreign License, Rating, or Medical Certification
and fax them back to FAA and CAA (CAA will charge you about £40 for the priviledge), you need to start this about 90 days before you are due to go, mind you if you fax the forms it will happen a lot quicker, mine took two weeks.
There is no night rating just a night qualification, 3 hours dual, 2 solo, although I think if you don't have this they can mark your FAA license with a no night restriction.
2, Correct
3, Correct and yes you need to get an I-20 off a school to start the visa process.
Last one is wrong, you need to have at least the FAA based on license to fly PIC in the US.