I assume you have another source of income, like a full-time job right? If that is the case, you can report whatever your Adjusted Gross Income is on your tax return. That's what a lot of people do. If Amex ever asks you to prove your income, then your tax return will reflect that reported amount correctly.

It is my understanding that if you apply for both cards on the same day, it will be one pull. I am not 100% sure, but that is how I understand it, and that is how it has worked for me in the past.