Definition of Rights Purchased

One time rights means you still own the rights (all rights is where you sign away the copyright to the publisher). As for the simultaneous printing, you'd probably not want them to appear in current/future magazines unless the book is cited once the book is released...as long as the book publisher is aware of where they have appeared (and where any may be scheduled to appear between now and the book release) it should be ok, but I'm no expert on this stuff. Maybe someone else could add anything I've missed.

Is the publisher ASKING you to put the earlier works in the book as a series of essays, or are they wanting something shiny new? That's the first question you should ask, IMO. After that, then yes--one time rights means just that. You can use the rights for other purposes. What many authors do for the purpose of crediting is to make a glossary of the articles in the back that shows the title of the original piece (which may or may not have the same name/chapter title as in the book) and the magazine. You can call it "First Appeared In" or "Originally published in" or something like that.

BTW--congratulations on the book offer!