For the first question, you can apply Category A if all of the following apply:
1) He is STILL employed at his US job on the date of application, and he has been earning at least £18,600 at that job for a minimum of 6 months
AND
2) He has a job offer in the UK paying at least £18,600 and starting within 3 months of the application date
In this case, you only need to provide 6 months of payslips and bank statements, along with the job offer confirmation and/or new contract.
If he has left his US job by the time you apply for the visa (or has not been working there/earning £18,600 for 6 months), you will need to apply under Category B instead.
For Category B, you need to show:
- he has earned at least £18,600 in the US over the last 12 months
AND
- he has a job offer in the UK paying at least £18,600 and starting within 3 months of the application date
For Category B, you provide 12 months of payslips and bank statements, along with the job offer confirmation and/or new contract.