I have a very general question. Say I have written 10 papers, published them independently in different journals over the years - could I then just take these papers and make a book out of them and publish that, or is there then a copyright on the published papers which would prevent me from doing that?
If you just want a compilation of your published papers in book form, I don't see how that's publishable, since it's all already published. You could probably find someone to create such a work, but not one that could be officially published.
If instead your intent is not to copy and paste the papers as a simple collection, but rather synthesize your corpus into a coherent, complete review, that's different. Nothing would prevent you from doing this - pretty much anyone can publish a book these days, though more established publishers would be preferable.
You'd need to get reprint/copyright authorization from the journals who own your papers, but only if you plan to reprint figures or in some cases, large sections of block quotes. Otherwise, a synthesis is a novel piece of work no different from anything else.
It is very likely that you would have assigned to the journal publishers the copyright to some or all of the papers you published, so you would not be allowed to publish the book without getting permission from those publishers. With that said, book anthologies of previously-published scientific papers are fairly common, and my understanding is that journal publishers are generally inclined to give their permission for a paper they hold the copyright to to be published in such an anthology.
A separate question is who would want to publish your book anthology. Unless you are a famous academic, I don't think such a book would be of interest to mainstream academic publishers, regardless of whether you need or can get the necessary permissions.