When you say 1,001,000, do you include 'and'?

"And" is only used after the hundreds (three hundred and twenty-five). Quite a few Americans will say three hundred twenty-five, especially in formal settings, because we had it drilled into our heads as children that and indicated the decimal. In practical terms this only ever mattered when writing a check/cheque, and it usually goes unnoticed in speech,

Otherwise there are no "and"s : "one million, one thousand."

(If you need to actually use this number once in your lifetime you have been very lucky)