If the book is A4 then the cover is A4+Spine+A4 = so that would be 210mm+Spine+210mm = 420m+spine
The thickness of the paper is not the only contributing factor! What about the glue! Is the book threadsewn? If so then you need to add about 1mm extra for the glue and an additional 1mm if it's threadsewn!
YOUR printers will be able to give you the accurate spine width based on the paper used. They'll actually use blank pages, fold it, glue it, (threadsew if needed) and measure the width of the spine for you. They do it all the time it's what they're there for :) Don't be afraid to ask your printers questions! It's imperative they are involved.
In regards to working on the file.
I find it efficient to take all the book into one document, that way I can keep the styles and other things pretty neat.
Depending on the project, and how many chapters, and if I have a lot of running heads/chapter numbers or other things, I will split the document up into Chapters AFTER I've finished applying all the styles and treating the text.
It's much easier to find all those little errors, like hyphens instead of endashes, and double spaces etc. This is what I like to call the RAW file where I'm just parsing it through lots of find and changes to speed up the process.
One book I do has 2 running heads per page, includes the chapter number in the title aswell. It was necessary to break this book up into separate chapters and work from the book file. And it was over 3000 pages. So it was a must.
It all depends on the content really.