The supporting evidence that you would file would be birth certificates, marriage certificate, divorce certificates if either of them have been married previously, proof of the spouse's U.S. Citizenship, proof of her legal entry into the U.S., and financial documents of her spouse to prove income over the last year at least.
In about 3 to 5 months after filing, she should get a work permit. About 5 to 7 months after filing they should get a marriage interview. If all goes well, a few weeks later she should get a Residency status (green card).
As far as the children, the can file an I-130 for each of them because the Priority Dates are current, but that could change any month. It may be better for the step-father to file an I-130 for each and that would process as if they were children of a U.S. Citizen. Here is a link to the process:
Unfortunately, it will take about a year for them to immigrate unless they have some extreme emergency. Here is a link:
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