Ultimately, it depends on who's printing the job. That person produces the book. Everyone else in the process is just setting that up, and should be tailoring their input to whatever's going to be the end product.
I don't know anything about Euro-sizes, but 5½ x 8½ inches, 6 x 9 inches, 8¼ x 10½ inches and 8½ x 11 inches are all common page dimensions for books produced in North America. Your book project may use any of these sizes, or none of them. You want to start from who will be printing the job and how, then work backwards. If you don't, I'll just about betcha you'll be doing it twice.
As for who decides how the book will ultimately look, that's between you and your client to work out. If you're working for a publisher, often a designer or production manager will specify how the book should look — fonts/leading, sizes, typographic flourishes like drop caps, dingbats/dividers, ligatures, etc. You'll often get specs and/or a template, then fill in the content and fine-tune it as necessary. If you're working with an author, you may get that kind of detailed direction, or not, or a confused and horrified look like you've just grown a second head while asking your questions.
As for text, it'd be great if the author provides you the text as individual chapters. Don't count on that happening. But even if the author doesn't do that for you, do yourself a favor and break it up yourself before you start laying out the job.
As you're learning more and more about this work, you'll likely realize you want to define exactly what the end product will be, then work backward to define to the best of your abilities what's going to happen when, and how much effort by whom is necessary to get you there. And nail all that down to the best of your abilities before you start — or if you plan to do this for a living, before you tell a client what it's going to cost in your proposal before accepting the job.
That's important for deadlines, for planning how you will meet those deadlines, for budgeting what it will take (and if you're in business, what you're going to make) to do the job. And most importantly, for setting realistic expectations for what can and will be done to meet your client's goals.
Consider how this applies to what you want to do. Good luck, and welcome to the joys and miseries of being an independent graphic artist.
Randy